damn autocorrect...

You can actually SEE if they've revealed the key. If they've done that, then I'd get anxious.
Otherwise, they are allowed to take up to 7 days to mark it received, so no point getting anxious.

EDIT - go to the specific giveaway, and then click on "winners" - it shows if it's been revealed with a green eye.

Absolutely, I did my first giveaway yesterday and I started feeling like that after 20 minutes 😧

I had a winner recently that was online multiple times every day. On day 6, I sent them a message on one of their previous giveaways reminding them that they won my giveaway and they are supposed to activate it within 7 days. They were still marked as online multiple times when I checked throughout the next couple days and didn't activate the game or respond to my message. I also saw on the winners page that they didn't view the key. With almost 400 wins, they clearly know how the site works, so I figured they are either using a bot and haven't checked the site in over a week or they just have no interest in the game or talking to me, so I requested for a new winner.

I wouldn't say it made me feel anxious, just curious to know why they are online every day, but don't want the game they won.

anxious? no.
I do get annoyed if I have seen them be online 50 times since sending the key and they haven't revealed the key yet.... to the point I have to request a reroll after a week(I will be more patient if you haven't been online).

It give a lot of autojoiners (bots), so the owner of that account only appear each 4-7 days to check if he win something.
This accounts get on and off all the time, enter new GAs etc..
Nothing you can do, besides setting a minimum level restriction (higher as 2).

And of course have some normal users not everytime, when they look into sg, the free time to activate their win directly.

You can't do something against the 7 days waiting time, so try not to have a bad feeling when someone take longer to activate a win.

Maybe reward the people that don't take 3-7 days to do it or the ones that do it in under 24h. As example with a whitelist.
Maybe that would close out a lot of the autojoiners from your whitelist.

As soon as a giveaway ends and maybe even before that, I get very stressed, even when the person didn't even came online yet, that's why I rather do short giveaways and be done with it since it's so stressful to me to do!

One of my keys got activated about 9 days after the GA ended, and days after the winner logged in and was aware of them winning (plus me sending a message about it as well)...
it happens.
With another GA of mine I forgot to check, and I got a cheery message like 2 weeks after it ended, the winner being super happy that it wasn't rerolled, as they were on a long vacation and forgot about the site.

Do no worry or really trouble yourself before 7 days passes. Even then, you can talk to the winner if there's a problem. Worse case scenario, key doesn't work and you delete the GA. Worst case scenario, you'll have an undelivered gift to your name, which can happen and it's fine. As long as it's sporadic and there is no malicious intent behind, you won't get punished for it.

This said, I'm still a bit stressed and tensewhen I do a big batch of giveaways, and double or triple check if I copied the correct keys, if I checked the winners, if I hadn't accidentally doubled-up a GA... but you'll get used to it a little bit more if you spend more time here.

waited a few months, one time. bud was hospitalized, i wasn't aware.
he was happy to redeem it.

I will not name names here but there was once a winner that didn't mark my GA as received until more than a week after it ended, and during these days they were frequently online and kept entering more GAs (I could see the counter going up). It was agitating for me.

Setting minimum levels a bit helped me to not wait days till lazy autojoiners come confirm status. Level 2 is a must, but now I barely go under 5+.

Not really, i sometimes take a day or two to activate a win just because i'm busy with other things. I figure other people have their own lives as well... Maybe if they actually take close to the 7 days they have within the rules because it'd be a bit of contact them and/or request a reroll.
The only times when i can see a bit of reason in being anxious about how quick they are to activate a gift and give feedback is when you're trying to push your CV to the next level quickly or if your GA-slots are actually all occupied and you wanted to create new ones after those finished.

You are new, so that's a normal feeling. But once you made some dozen or more giveaways you'll barely even notice.

Nope.
People have 7 days, just like you have 7 days to send the key. Would you have liked to have people judging you if you took like 5 days to send a key because you missplaced a key, or because you had a family emergency?
Seeing someone online doesn't mean that, that person can redeem the key, since many people use the App on mobile, the app doesnt allow for a easy redeem.
People might just see they won and wait until they are in front of a PC to redeem the win. No big deal.
You just need to take care of that feeling :) If the key fails, people will just tell you... why would they not? Why are you worried with the key failing and they not telling you? It's their problem if they don't activate the key.
Just chill, people have lifes and problems. No point for you to even worry about that. The rules are there to protect you. Trust the system, works most of the time. If it is a autojoiner, just wait for the 7 days and reroll, maybe it goes to someone else that will apreciate the game more :)
Trust SG system rules, they are actually well thought up :)
And boy if you are this anxious with people failing to redeem keys, can't even think when you start getting blacklists left and right. :) (Spoiler alert: Don't open a discussion on that subject!)
It is a stupid comparision, I know, but Imagine you giving a christmas present to someone on the 20th of December and being anxious because the receiver waited until day 25 december to open the gift :)
Enjoy your stay, this is not the place to ever be anxious, mad or nervous.
Welcome to SG!
Also, take a look at "Unlucky-7" and "Playing Apreciated(think recruitment is closed now)" groups, they are a nice way to start :)

Edit:
Advise: Just stop checking if people are online, it will probably help. I never did that on any of all my sent gifts... Yes, people are diferent, but maybe you can try to avoid checking that, it will help you build trust on the system and probably help with the bad feelings.

hmm once you start giving away games on a regular basis, you won't get anxious but be a little annoyed. just wait for 7 days and check if the keys are marked as received or not. if it's not marked, check the winner's steam library to see if he/she has activated the key or not. if he/she hasn't activated it, then drop a message on his/her steam profile(if you can). else, go to one of his/her hosted giveaway and tell him/her that he/she has won your giveaway. if he/she doesn't respond within the next 7 days, take screenshots and ask support for a reroll.

I can only speak for my experience but there can be legitimate reasons for someone appearing online after winning a game. In my case 99.9% of my time on this site is via a mobile browser and very often I only have a few small breaks or windows of opportunity during the day or even evening to pop in here and do some quick entries and then get back to work or other stuff.
On the occasions when I've been visited by Mr Spacecat, very often those giveaways are won in the middle of the night my time and I have precious little time most mornings to properly deal with it. By which I mean devoting the time to review the GA (in some cases jog my memory of entering it if it was a while ago!), revealing the key and activating, checking it's fine in Steam and posting a quick polite thankyou to the GA page unless indicated otherwise and finally setting the received status. I prefer to spend a few dedicated minutes without distractions to get it done properly but that often means waiting till the evening my time or even the next day if I'm really busy.
During this time I pop into the site for a few seconds throughout the day to enter GAs and check some forum threads, all the time seeing the flashing icon telling me I'm a bum to get a move on. Complicating that is often I leave train or puzzle pages open on my mobile browser during the day for hours at a time to pop in where I can, creating the impression that I'm online much more than I actually am!
That said I always try to deal with the GA within 24 hours as a mark of courtesy to the GA maker but I admit sometimes it's more like 36hrs, one time almost 2 days 🫢, for which I always try to apologise for my tardiness, even if it is within the site's grace period. I wouldn't stress too much, most of us lead hectic and busy lives and I imagine 99% of people are thankful for the win, they just need to find some time to deal with it properly.

I used to in the beginning when I had too many games to give and too few giveaway slots. Not anymore. If it doesn't work, then it doesn't work. No big deal. I do start to get anxious if it's a week or more, because I hate chasing down winners.

I find the "too busy with other things, that's why it took me so long to claim a win" statement rather stupid. You weren't too busy to enter a giveaway so you should have the spare minute to check your email once a day for a SG win notification provided your account email isn't obsolete or you're using an autojoiner.

Having to wait days for a winner to activate a key doesn't instill anxiety in me but annoys me. Of course there might have been an earthquake or a volcanic eruption or another major calamity in your life. If this is the improbable case I apologize in advance for misjudging the situation.