I got OS/2 Warp 3.0 (blue version) installed on my Pocket386 and it is working well! It has been well over 20 years since I last used OS/2 so I've been recalling some old info that I forgot all about. This version of OS/2 has DOS and Windows 3.1 compatibility so it is a pretty flexible environment.
I used a VM to install onto an 8GB CF card. OS/2 3.0 doesn't like large (>2GB) disks so I used FreeDOS to partition it, and found a patched OS/2 install floppy online that uses a newer driver that doesn't barf at the partition table. (Be careful not to overwrite that driver when installing the Fixpack later on!)
Graphics work fine in VGA mode. There is a Cirrus Logic driver that works, but that broke video in my VM so I kept it on VGA for the sake of convenience. I couldn't feel any performance difference (neither is accelerated 2D). I tried installing the free Scitech Display Doctor drivers, and they dramatically improved performance in my VM, but unfortunately on the Pocket386 they just cause it to crash at startup, so I reverted to VGA.
I upgraded it to OS/2 FixPack 40 from IBM's FTP server which is still online after all these years and everything is in the same directories!
I wasn't able to find any working sound drivers. There is a Yamaha OPL3 driver online, but either it wasn't the right one or I didn't configure it correctly (no plug & play). The PC speaker beep works though.
The speed of the virtual mouse movement is quite slow, but this version of OS/2 is pretty keyboard-friendly so the mouse isn't really necessary. It is impossible to drag & drop with the virtual mouse anyway.
I installed Object Desktop 2.0, which adds lots of creature comforts and features, but it's simply way too heavy. The startup and general usage of the system became very sluggish once it was installed and the CF I/O was nonstop due to swapping. I remember on my real PC back in those days I did not have enough RAM for it, either. So, I removed that and things are back to decent speed.