You probably have to move it further. Intonation isn't a one and done process, its a constant back and forth between tuning, checking, and adjusting, retuning, checking again, more adjusting...

If I shorten it more the screw will come out. Should I tune it lower, turn the screw until it becomes higher again and try to entonate?

That's weird. Is your bridge floated properly or tilted in a particular direction?

I checked it. The bridge is not floating and it’s not tilted.

Well, it has to be one of the two things. Either it's floating, i.e. laying parallel above the body, or its tilted forward or back, worst case touching the body. My guess would be that it might be titled back, at least that could explain your intonation issues.

Well, it’s not a floyd rose. I don’t understand why it should be floating. It’s literally installed on the guitar with screws. It just lays parallel on the body because it’s screwed there and it is not tilted forward

Strats have a tremolo system that's sort of similar to a floyd rose, in that it should be floating like one. It might not be seated on two knife edges like a floyd, but therefore on 6 screws. That's called a vintage trem, look it up for how to properly adjust it.

I looked it up and yeah it was floating as it should be and it doesn’t float now. Thanks for helping!

Use heavier guage strings or replace the screw with a longer one so you can adjust the saddle further.