Thank you, everyone, it seems that a bleach (potassium-based) was a problem indeed. I've been agitating lots more now. I've also noticed that the FOMA instructions on mixing are slightly different in English/Czech and German, so I tried the German version with reduced volume and tested several strips. It's so much better:
I've developed 5 test strips, first following the German mixing instructions and times, and then adding 15 seconds per test to every step because I also wanted to see if you can reuse the chemistry. It seems that black is a lot deeper when developing times are a bit longer, even the 2nd one. But then again, the 3rd one came out almost clear. It looked great during 2nd exposure, but suddenly that yellowish color went a bit darker, which was odd. Still, I've continued with 2nd developer and fixer anyway just to watch the emulsion wash away in the end. Can you over-expose the film during the re-exposure?
Then I did two more, all good. And the chemistry still works. Does it mean it would work in a large volume and with full-length film? I don't want to find out with serious material 😱. I've read that developer can be tested on an exposed piece of film, is it possible to somehow verify if the bleach and clearing bath still work too?