Can we get an option to block someone in the trading section?

Well, the thing is that you are I think considering the giveaways section to be part of the "forum" section.

What I was discussing had nothing to do with the interconnectivity of site sections;
I was saying it was silly that you can prevent people from communicating with you where they may actually need to [ie, to follow-up on a giveaway they won], but not from spamming your trading thread, where they ought have no basis for needing to continue to contact you.

it's only normal that the blacklist wouldn't work on trades, because it doesn't work on discussions either.

Trading presumably works off the forum system instead, which does not limit access to blacklisted users.

Moving on..

Either way, a fully implemented block function would only increase the amount of drama I think, imagine all the threads of "You can't access this discussion/trade because you have been blocked by the creator", the same way we get those about being blacklisted in giveaways constantly.

For discussions it's unwarranted, as they're public discussions.
(While there's no reason the OP ought have to suffer the inbox notifications, there's also no cause for excluding individuals from topics relevant to the community at large. Given that vetting each thread for 'importance' is unreasonable, simply not applying the block from blacklist is the only fair option.)

Trades are direct correspondence with the creator, so there's no basis for not being able to ignore users.
Your drama point is nonsensical to me, in the context of trading ignores:
First, the individual'd have no way of really pushing the matter outside of methods that'd also get the rest of SG (completely understandably) irked with them, same as with blacklist bitching threads.
Second, we can't take away the respect and rights someone else is due, just because the individual behaving inappropriately might continue to do so in a different way.
The individual doing the blocking is in no way responsible for the person being blocked acting in an inappropriate manner on the forums because of it.
Thus the question becomes one solely of 'Does the user have the right to prevent being harassed', and the answer is yes.

User in your ignore list still can enter your trades and discussions, and even comment, but his comments or threads would be automatically hidden by default, and you won't get notifications from it either, so it wouldn't bother any of you two at all.

I've pushed for this functionality several times, myself.
Combine that with harsher punishments for people that massively spam or deliberately harass/bully/insult, and you'd potentially be able to weed out most of the antagonism on SG.
(Though in fairness, from my impressions, staff seems to have cracked down a lot, lot more on that since back when I joined, so I really don't know if I still have grounds to push that last point.)

My favorite approach to blocking functionality has thus far been as follows:
No notifications whatsoever, and all comments made by the individual show as condensed- so you're still aware of their presence and still have the option to view them if you feel you need to, but otherwise won't have to deal with them.
Add in the extra option to hide threads from a user, and you could have complete control over managing users that simply won't leave you alone.