I can't thread when the spindle is higher than 600 rpm

Maybe spindle.0.at-speed is not true?

When should this be true?

wow...

linuxcnc.org/docs/html/examples/spindle....sec:spindle-at-speed

You were right, this was the problem. The difference in my near was too small and the actual spindle speed is a bit above the commanded one. For 1000 rpm it was actually 1020 and for 1500 it was 1527 so it was considering not at speed. I increased the difference from 0.1 to 0.5 and now spindle-at-speed is true.
However I should do some lincurve or pid tunning so that the commanded velocity matches the actual velocity.

Thanks for pointing this out, I would have never figured this out.
I also noticed that I was a bit too ambitious and I added an and that will set the spindle-at-speed to true if the spindle is on and the target velocity matches the actual velocity. I added that condition because I saw spindle at speed lit on when the spindle was off, because they were equal.

Do you see any problem with that logic being there? Do you see any side effects for this?

The spindle at speed lit on when the spindle is off is many's fav feature of lcnc. Can't be more accurately correct!