Has anyone else experienced unusual slowness in SteamGifts in the last few days? (a week?)

It's likely a steam api thing. Api costs have went up overall, so I wouldn't be surprised if steams have too, and they've done multiple things recently to mitigate costs, which likely results in slower response times. That, or with the new api changes, they're using a bad method to fetch stuff which is now slower.

Yes the slowness is on the server side.

And just to be clear, when I mentioned "caching" I was not talking about browser caching, but caching of the intermediate results that happen on backend server-side (like caching expensive database queries), invisible to the user.

If you look at the page, you will see it is served with HTTP headers that explicitly instruct the browser NOT to cache it:

cache-control: no-store, no-cache, must-revalidate
expires: 1981-11-19
pragma: no-cache

which makes sense given the dynamic nature of the page (it needs to list giveaways entered by user sorted by end-date, along with current total entries to each GA).

This is definitely NOT a network related issue.

No.
And this is definitely not related to any Chrome extensions - As I mentioned it happens on backend services accessing SG as well.

For the first time? Or after that?
As I mentioned:

300ms once it's cached

So once you've opened it for the first time, it's cached, so it doesn't really load fully.