Your question is a bit of a paradox. The simplest answer is to say that you can't. "Gaming" just means using the propriatery software a company built, and online gaming also means connecting to their server (unless you emulate your own, but that's becoming more rare these days).
But the longer and more fair answer is to say that absolute privacy isn't necessarily realistic or desirable for all, and you are looking for the best compromise that works for you.
If using linux is important to you, I think valve has been doing a very good job porting a lot of their library and making it compatible with linux through proton. I used that for a while, but I have to say I didn't like the bunch of random files games would pollute my system with.
I guess my suggestion would be to have a dedicated system for gaming (either by dual-booting, or a vm with pci passthrough for performance, or a different system altogether like another pc or steam Deck). Only use an identity meant for gaming with that system, and keep practicing a healthy separation of concerns there.
Finally as a game dev, I will invite you to not pirate games you like, especially from smaller creators.
I haven't seen a lot of hate on it coming from regular people, but rather from those who try to cultivate an audience online. Content creators, influencers and others alike seem to see mastodon (and potentially any decentralized system?) as worse because it inherently prevents them from being guaranteed to be reachable by the whole community all the time (in case of defederation for instance), or to migrate their following along when switching instance
I imagine you think this because of medical things (heredity and all that) AFAIK It isn't used for such things, only for legal responsibility (adoption for instance would modify it), so in order to protect the position of those who actually raise the kid and the stability of their family, I don't agree with you. Not without changing the role of the birth certificate first at least