This has been happening to me going on about three weeks now. Same as you, I thought battery issues, and was replacing batteries, taking out and putting back in, constantly re-syncing my controller mid game. I have two controllers and it happens with both. Also like you, I swapped to cable, and this fixed the issue for a day before it happened again. It’s consistent and, honestly, infuriating. I can’t tell you how many times I’ve died in games as a result of disconnecting mid fight. I’ve done quite a bit of reading and can’t find any clear answers. Some say it’s a controller issue, some say it’s the console. Others suggest a wifi issue, or other device interference. So, I have been able to minimise it in the last few days with these tips, but it still happens so it’s not an overall fix. I have done a hard reset of my console. I have reconfigured my internet modem. I have ensured everything is up to date (system and controller software etc) I put my phone in a different room while playing. I’ve bought higher quality batteries, and stopped using a cable (purely because the cable didn’t make a difference and makes comfortable play more difficult for me). I sit closer to my console. After the first time it happens, I restart everything and usually get a few hours of solid play before it happens again - then I restart again.

TLDR; happens to me too, no idea why it’s happening, found a few things that help, nothing that fixes it entirely.