OK, I went a somewhat simpler way by patching and recompiling only tplink-safeloader and repack the image with it: Port to TP-Link RE200 - #124 by 999cgm
And it worked! I flashed it through recovery mode, but I guess it would work with the normal WebUI too.
So the line is the same as I mentioned:
{product_name:Archer AX23,product_ver:1.20,special_id:52550000}
I found an instruction about sending patches, so I will try to do it somewhat later. But for now @FATALI @Unworried3946 - you can try to patch tplink-safeloader.c manually with this line and follow the instructions I mentioned to patch your images and check if it'll work for you.
@Borromini thank you very much!