Which Sennheiser headphones do you recommend for a newbie to audiophile stuff? (Though, mostly for gaming)

As the title suggests, I'd like to start getting serious about my audio, and I'll primarily be using them for AAA/ cinematic gaming. I like to shop at Microcenter and at my local store, I saw they have the HD 569's and the HD620S's, so I was wondering if these were good, or if any of you recommend other/ better headphones. Price isn't too much of an issue, but capping at ~$300-350 would be nice.

My first "real" headphones where the Sony XB950B1's, and I especially loved them because I was a sucker for the extra bass back in high school. I thought they were fantastic for listening to my favorite Rock and Rap songs, and looking back: I really miss the nice-feeling rocker switch/ button for pausing/ playing, rewind, and forwarding, great mechanical engineering for a really great feeling switch.

Then I went to air pods for a little while for the convenience, then halfway through college I was like "you know, lets just go to best buy and see that they've got," and I went back to Sony again with the WH-XB910N's. I currently use these headphones to this day, and they're still a joy to listen to, however they're starting to get a little old/ used and again, I've been itching for an upgrade. I've had to buy replacement earpads, and the headband is slowly starting deteriorate (I suspect cheap material).

Back to my use case, I just bought a new PC and got Resident Evil Requiem bundled with the GPU, and I have other high-budget AAA titles in my library, including Doom: The Dark Ages, Red Dead Redemption 2, other Resident Evil Titles, Batman: Arkham Series, Forza games, etc. My motherboard - like most - has a 3.5mm audio jack, and since I've seen that 3.5mm has better quality/ accuracy than Bluetooth, I'm not too interested in headphones that have Bluetooth connectivity. Plus, I'll still use my Sony's for when I'm not at my PC (gym, doom scrolling on the toilet, etc., lol).