Got something done today.
Followed Kent’s suggestion and made three UV maps now; one for the floor, stairs and support beam, one for the walls and one for the rest.
Also reorganized the outliner a bit (still a mess, because almost everything is called ‘Cube’, but at least they are in separate Collections, so I can easily hide the floor, for instance).
Then started painting (again!).
This is how far I got today:

Didn’t do the metal pieces yet, just the wood.
Tomorrow I hope to do the walls and then on Sunday the crates and the barrel.
As the barrel is the main character, I’ll do that last, when I have gathered some experience in painting textures;)
I especially exaggerated the contrast in the wood; it’ll be easy to reduce that in the shader if necessary….