I tested and this is what happened

[gmp50]

I tested it on picow because it was the easiest to use.
I connected the USB port because I thought both would work if they automatically detected the port or Bluetooth, but they didn't

Bluetooth
On PS3
All the controllers go crazy when you enter a game and show low battery, in the menu it works fine

On Switch it works fine but:
PS4 - has a notable input lag
Dualsense - less input lag
Xbox Series - Almost doesn't feel input lag

Wired (no input lag)
On PS3 sometimes show a message that battery is low with all the controllers
PS4 - the home button doesn't work
Dualsense - sometimes it doesn't work well and goes slightly crazy or some button doesn't work (this happened to me in MGS3 PS3)
Xbox series - sometimes it doesn't work well and goes slightly crazy or some button doesn't work (this happened to me in MGS3 PS3) the home button pretends to be held down for too long and the menu appears instead of the XMB

Nintendo Switch (no input lag)
PS4 - The home button doesn't work
Dualsense - Works without issue
Xbox Series - The home button pretends to be held down for too long and also takes screenshots or videos

Extra
I tried the Hatsune Miku Project DIVA Future Tone DX Mini PS4 Controller and it works perfectly.

I hope my report helps, even if it's not very detailed.