There are versions of uLaunchElf (maybe the fork wLaunchElf) that have drivers for more controllers like DualShock 3. The drivers are optional because space is tight on a "Memory Card(TM) (8MB) for PlayStation(R) 2".

I have two of these and they work wonderfully. It comes with a pairing guide for specific controllers, and a full list can be found here.

You should use wLaunchELF_ISR over uLaunchELF for better compatibility and functionality.

From the AliExpress page under NOTICES:

2. The power supply of some old PS1/PS2 console controller interfaces may not be normal due to some reasons, causing the Mini PS1/PS2 Blueretro converter to not work. In this case, you can use the micro USB port to power the Mini PS1/PS2 Blueretro.

I actually didn't know that's a thing because the adapters work on both my fat models and my slim.