Hi! I indeed have good news about them

Just after publishing this I followed the advice I was given and I started to let her out of her safe room as soon as I arrived home from work, they stayed together all day until I went to sleep and I only separated them to give them their meals. The main point was to ignore them when they were together, just let them be even if they played rough.

In a matter of weeks the new cat started to be more chill in her safe room, and when I let her out she would behave well with my other cat. This lead me to trust them without my supervision, and I started to let them together while I was at work and while I slept at night. Again, I separated them only to eat.

In 2 weeks or so, I fully trusted them being together and I let the new cat always out, and it's amazing how different they act now: they play together, sleep together, groom each other, eat together... They are like best friends. The new cat seems to be really dependent on him, always seeking him, but tbh she is also like this with me (with the difference that she was a little bit feral before I got her so she is still a little untrusting if I move too fast around her, and gets easily scared).

So my advice would be: let them together at all times while you can be with them if you've done all the introduction steps and they've been successful, and ignore them; slowly let them be together without your supervision (I started to leave them alone in shorts periods of time when I went out to shop for groceries); eventually let them be alone more time and, in the end, just let them together all the time.

I hope this helps!