I'd first tell you to test things out yourself instead of just blindly following recommendations - lots of F2P games change constantly and what used to be good can be pay-to-win today. Check out Steam or the Epic Games Store and read through the current reviews, especially the negative ones, that's where you'll quickly find out if the monetization is annoying. Plenty of people complain there explicitly about pay-to-win mechanics, so you can filter that out pretty easily.
What's still running solid right now: Valorant is basically just cosmetics, the actual gameplay isn't pay-to-win. Team Fortress 2 has been around forever and it still works, even if the community is a bit thin sometimes. Dota 2 unlocked all heroes without paying - only skins cost money. With these three you can actually play without feeling ripped off. Path of Exile is pretty okay if you're into loot-hunting, but you gotta be careful not to fall into the trap of convenience items.
The thing is: pretty much every bigger F2P game has some annoying mechanic, whether it's battle passes, energy systems, or hidden pay-walls. My strategy is to just start several games and check after a week whether the monetization gets to me or not. If you notice you're constantly staring at the "pay now" button, it's time to move on to the next one. The really good free games are the ones where you realize you're paying voluntarily, not because you have to.