Hello, I realize this is a bit daft of me, but any help would be greatly appreciated to help me figure out the easy way to capture game footage/audio from my consoles from my current setup?

I have all the things , a PC/PS5/Xbox and Switch

Setup: for clarity, My pc is in a separate office room and my consoles are connected to my home theatre with a receiver / ARC connection to the big screen tv.

im trying to figure out what i need to capture footage. so like , oh im playing the latest ps5 game , lets connect this device have a session and record. cool im done recording "take the device to my pc" grab the video files and edit, Is that even possible? then easily swap to xbox if im playing the latest thing there?

the googling/youtubing i have done, seems everyone is doing this from there giant stream type setup where everything is connected at one desk so im just a bit confused if its possible to capture straight to a storage device or something? or would I basically need to bring a console over to my pc setup so the pc can be landing for the video files?

thanks just trying to make sure i understand before buying anything :P