Substructure Alignment (Wood-Wood)

Basically, good solutions have already been mentioned, what I would additionally recommend is a simple cross-line laser. For short distances, there are already relatively inexpensive devices available on the market. Set up the line laser in a corner, adjust it to any height, and mark a control crack at a few points in the room. Now simply measure the distance between the laser and the ceiling with a tape measure. Once you have found the lowest point of the ceiling, attach the first batten there and align from that point. If you use the laser for this, you actually don't need a guide batten or spirit level. When the batten is at the ceiling, take the measurement from the laser to the lower edge of the batten and set this measurement at every point where you screw the battens. Whether you use spacer screws or place shims and anchor directly is a matter of preference. You can then screw the load-bearing battens directly onto the counter battens.

Thank you for the answers,

that's exactly how I did it. I bought myself a 360° laser from Bosch. The thing is simply made for that.
Then I attached it to the wall and turned it up until it had the first contact, (That was logically about the middle) then I had my lowest point.

On the sides there was about 3-4 CM difference to the middle, there I removed the old battens because they were only 2 cm thick and put on a 4x6 cm batten (New basic lathing), if I now put a 3x5 batten on top of that, then I have a deviation to the middle of 0.2-0.5 mm and I can then align that perfectly with adjusting screws. Everything is rock solid on the sides, even better than on the old lathing.