I managed to open it using just big wrench.
So I have a screw sticking out inside of the bracket socket. It's from the plastic cable holder on the bottom. I guess I will have to remove it if I install a new cartridge sealed bracket.
I think I understand it now, so in order to install a cartridge BB I would need a special tool for that one. But no more lock rings.
There are so many of these BBs out there, different sizes, with or without bolt, I would need to figure out which one I need at all. At least for that bolt thing.

I have 68x118 bracket size, just need to figure out what interface and what threading it uses. Probably English. It looks like JIS but also a bit like ISO, I'm not sure.
I think any should fit those crank arms anyway.
I think this one should work well:

https://www.amazon.com/Shimano-Squar...ket&th=1&psc=1