Logitech's latest Astro headset has a built-in HDMI switch

The Astro A50 X gaming headset comes with Playsync technology, which is kind of like a HDMI switch with the headset as the remote.

Logitech G Astro A50 X Gaming Headset Review: A Multi-Platform Maestro

Logitech G Astro A30 Lightspeed Wireless Gaming Headset - Bluetooth, Dolby Atmos/3D Audio Compatible, Detachable Boom, 27hr Battery, for PS5, PS4, Nintendo Switch, PC, Android (Renewed) : Video Games

Logitech Astro A50 X review: The best, most expensive gaming headset - Reviewed

Logitech made the ultimate gaming headset, but it's complicated

Logitech G Astro A50 X

ASTRO Gaming

Logitech's Astro A50 X headset can switch between PS5, Xbox and PC with a button press

Next-gen Logitech G Astro A50 X headphones boast HDMI passthrough switching between gaming consoles and PC audio/video - Yanko Design

Review: Logitech Astro A50 X Wireless Gaming headset gets almost everything right - for a steep price