How to avoid entering ga for owned games?

If this happens, I hide the game. (It's the eye icon on the giveaway).

I have seen personal cases where I could enter a goty edition of a game I own the base version for and vice versa. I usually hide those games from appearing from all giveaways list
as spookypankaka said, the little eye icon next to the giveaway's name

Personally, every time I win a game from here I go back to the GA and I hide the game. Realistically, there is no point to seeing the game again anyway as it's against the rules to win the same game.
And as for the profile features limited game, I go through my newer games like once every 2 months or so and manually type the PFL games into the search bar and hide alll the ones I have.
Otherwise, just sync your profile every time you get a new batch of games.

I use a script called 'Steam Web Integration' which shows me which games I own, ESGST also has a function like that.
Besides that, just hide every game you own here on Steamgifts, that also helps a lot so if you come across one that you already seem to have, just click 'hide giveaway' and you won't see it again.

With ESGST you can use the Hidden Games Manager to add all owned/banned games to Steamgifts filters list. That helps with DLCs and removed games. You only need to hide some special / GOTY editions manually.

ESGST can help with that.
One of the game categories from the namesake setting is "owned games" (8.2.22), which will highlight every owned item, including DLCs and removed games, since it relies on the private API endpoint (while SG uses the public one which misses a lot of stuff). You can then hide them manually when you see them.

...though for the first time it's probably better to use the feature at46 described in the comment above (I almost forgot since I had only used it once at the start).

If this has happened more then once it would be a good idea to check every thing you enter. If you cant recognise what you own then it will cause a lot of trouble in the future since who knows how many games you own that sg cant recognise.

I personally don't have that trouble since I only enter games that are on my wishlist, so as soon as I get a profile limited game it goes away in the giveaways too. Plus I recognise anything I own as long as its not free then I have no idea where those appeared!

Looking at above comments it might be a good idea to use esgst if you aren't keen on looking at every ga to make sure you want it / dont own it

https://www.steamgifts.com/discussion/y9vVm/userscript-steam-web-integration-previously-steam-store-game-owned-checker
It works fine outside of steamgfits also.

Only join GAs for wishlisted games ;)

https://www.steamgifts.com/giveaways/search?type=wishlist

I check all games before i enter them and can, mostly, remember at it months later too.
And i hide all games that i won or own, that nothing can happen if they get kicked from the store or the api change (or something like that)

I hide game I own when they come up but otherwise I look at the store page before entering.