How cautious should I be about a GA win being given as an HB gift link?

While it's not generally confirmed, the mentions of issues that originate from using gift links is on the gifter's side - too many different emails activating the games.

As far as I know, you as someone who just activates a key doesn't matter for HB.

Speaking as just a user here: as far as I know it's fine for you, the person taking a risk with this is the gifter: HB has banned people for gifting "too much" but not for getting a gift (again, as far as I know).
I've always used my "normal" HB account e-mail address in the rare cases where I got a HB gift link win, and didn't have any issue beside the terrible captcha from Hell. Also, I figured that at least when my e-mail is prefilled I don't have the risk of making a typo and locking me out of the gift 👀

The only major risks when Humble's supposed "gift" links are involved are on the gifter's side, as it's them who can get their account banned if Humble decides so.
As a winner and recipient, the only things you have to worry about are potential region locks, and the possibility of the key being borked, which would be rather tricky to fix.
By the way, your e-mail being filled out just means you were logged in.

And, well, if you also peddle in gift links yourself, I guess you might expect them to add it up to your presumed "trader/reseller activity"... I wouldn't put it past them.
Still, no real risks as long as you're not the one on the "active" side - and as long as you don't contact them (I think they don't just ban accounts on their own out of nowhere).

Thanks for your insights, everyone!