Can't get NVidia driver to work on Deabian 13 RT laptop

This also shouldn’t matter much in this case, but generally you need to do apt purge --auto-remove '*nvidia*' '*nvidia*:i386' '*cuda*' '*cuda*:i386' to really get a clean system.

so it seems it did succeed for non-rt kernel, but not for -rt that you use… Could you please verify this by running find in the non-rt modules folder: find /lib/modules/6.12.57+deb13-amd64 -name '*nvidia*'
If the modules are there, then it will be pretty safe to say that you’ve found a bug in Debian packaging related to -rt kernels and the best course of action is to file one.

In the mean time you can try freshly released Nvidia-packaged DC drivers for d-13: