@subs
In the meantime I tried to change libretro's (retroarch?) config (Hotkey+B), but it didn't work out:

There were different actions listed (like strafe left, shoot, dpad-left, etc.) which I then reconfigured very minimalistically: I modified dpad-left and dpad-right (right stick) as well as strafe left and right (left stick) and put shoot and use on the shoulder buttons.

Unfortunately this didn't work as intended: left stick left suddenly made the character move left and strafe left at the same time. What's worse, I couldn't revert the settings since now I could no longer confirm menu entries in libretro's built-in GUI even though I didn't remap any of the A,B,X,Y buttons. Really strange. (I didn't save the config to disk, so simply restarting prboom fixed it.)

I'd probably have to wade through all the docs in order to gain some understanding of all the intervening input translation layers (physical -> recalbox's SNES-inspired mapping -> libretro -> core). It seems daunting. At least it shows how great the team's work on all the integration stuff works in practice: all/most games are perfectly playable with only one centralized controller setup. Well done!

Still if anyone could point me in the right direction... 😉
I'll promise to write a mini-howto if I get it work.

I'll have a look at "Retropad w/ Analog". I think by default something about a "Retropad" was mentioned in libretro's GUI.