You might try to add the repository for it without using the script. I followed this page, but you can skip the rocm parts of it (except for adding the key). I managed to install it on Debian 12 this way.

I also have a 7800 XT and use Debian. I had to download firmware from git.kernel.org, as not even the package in unstable is new enough: stable has 2023-02-10, unstable currently has 2023-05-15, while 7800 XT (and 7700 XT) needs 2023-08-04 or newer At least bookworm-backports has a new enough kernel now. (6.5, IIRC 6.4 is the minimum.)

But to get ROCm working, I ended up adding AMD repositories and using its drivers with the 6.1 kernel from stable.