I dont have a ps5 but i have something that might help, on the ps4 i believe there was a simular bug where you couldnt connect your ps4 controller, what sometimes fixed this was going to the PlayStation menu, go to Bluetooth i believe and manually disconect and reconnect the controller again,(sorry if this is confusing my first language is not english)

Honestly i agree with the part of having a pc and a playstation, however i will admit that having even a mid range pc is still a bit expensive, i had to buy mine off a friend.