I'm wondering if there's a way to use Xbox Series X/S controller on PlayStation 3? It doesn't matter if they're wired or wireless; is this possible in any way?
It's possible via external tools, but the solution depends on what kind of firmware do you have.
Custom Firmware (CFW)
If you are using a console with custom firmware, you can use this plugin called PS3xPAD, It allows you to remap any HID compatible gamepad like the Xbox One/Series X|S controller.
Stock Console or Homebrew Enabler (HEN)
You will need to buy a 3rd party dongle that converts your Xbox One/Series X|S controller to a DualShock 3. One sunch example is the CronusMax.
This device makes your Xbox One/Series X|S controller show up as a regular DualShock 3 for the console, so it works without too much trouble. The way to configure them depends on the manufacturer, so remember to read the manual of the one you get.