
Sennheiser
HD 560S
Budget gaming king with clear sound, but tight fit.

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https://a.co/d/0amYMVn1 Epos h6pro. Epos has since pulled out of gaming I believe, but these are what's left and I've had mine for probably 6-8 years.
I've had my Epos (Sennheiser) H6Pro for years (at least 6) and still love it. They closed the Epos gaming division in 2023 but you can still get them on Amazon for $150.
Logitech G Pro X (wired) EPOS H6PRO (open or closed) HyperX Cloud Alpha (or Cloud Stinger 2 if on tighter budget) SteelSeries Arctis Nova 3 (wired USB‑C) the EPOS H6PRO is the strongest single recommendation. If you want to save more cash but still avoid trash mics, the Logitech G Pro X (wired) is the next best bet, especially if PC play and Discord are a big part of your usage.
They're effectively the old Sennheiser Gaming One with some tweaks, which were, indeed, great headphones. No idea why Sennheiser stopped making them in favour handing most of the branding to drop and going about doing something else. I've got the GSP 600, PC38X and a H6 Pro - all these are similar and they're all great.
Generally, snobby audiophiles will dismiss any gaming headset as bad. While yes there are plenty of cheap crappy headsets out there, there are a few stand outs and they've come a long way the past 5 years or so with some nice ones from Sennheiser/Epos (sadly discontinued), Sony, Audeze, and an ROG/Hifiman collab. Most wireless SteelSeries and Hyper X headsets have software EQ apps to tune it to your liking as well and they've made some nice ones the past few years. I hardly ever use a mic so I stick to headphones mostly these days, but I can recommend the H6 Pro (closed or open back, whichever you need). It's a surprisingly well done headset with inoffensive tuning, a good mic, and it's low impedance so a controller powers it just fine. They're discontinued but there should be old stock on clearance still available.
Cloud III is the best value out there and arguably the best for competitive gaming, the wireless version is great too if you stretch the budget. I can also recommend the Epos H6 Pro, either closed or open back. They're discontinued but there may still be some old stock on sale floating around. These are not wireless but soundstage is fantastic for a closed back.
i ran into this exact thing last year with a gaming-focused headset that sounded flat for music. at that budget, i'd look at the Audio-Technica ATH-M50xSTS, the soundstage is way better for music but they still game hard. the Audeze Maxwell Wireless is a bit of a stretch at the top of your budget but the planar magnetic drivers make music sound incredible. i'd also check out the EPOS H6Pro, they're open-back so the sound feels more natural for both. definitely focus on ones with good driver quality over just 'gamer' features.
I've been using the EPOS H6 pro headset for the past couple months. They've been super comfortable for 10+ hour sessions, even with glasses. It doesn't have any "gamer" aesthetic bits and the mic is magnetically detachable, so if you remove it, they're basically just normal-looking wired headphones. Mic quality is solid from what other people have told me, both while gaming and during work meetings.
I'm currently running the EPOS H6 pro. Sound great and are super comfortable , even with glasses. They're wired so you get solid sound quality and don't have to worry about batteries dying mid-session. They have replaceable ear muffs, mic and cables, so whenever those break or stop working due to wear, you can simply replace them instead of buying a new pair.

Sennheiser
HD 560S
Budget gaming king with clear sound, but tight fit.

Sony
WH-1000XM4
ANC king, durable, but unreliable mic and touch controls.

Sennheiser
HD 6XX
Legendary mids, durable, but narrow soundstage and weak bass.

Sennheiser
HD 490 PRO
Super comfortable, wide soundstage for gaming, versatile pads.

Sennheiser
HD 599
Super comfortable, easy to drive, wide soundstage, open-back.

Ranked #1
Sennheiser - HD 6XX

Ranked #1
FiiO - FT1 Closed-back Headphones

Ranked #1
Sennheiser - HD 560S

Ranked #1
Sony - MDR-7506

Ranked #1
Sony - WH-1000XM4

Ranked #1
Sennheiser - HD 560S