While (I think) you can install HWE (hardware enablement) kernels on Mint, you would also have to upgrade Mesa, which is not as easy on Mint.
Personally in this case, for a truly stable distro, I’d install Debian Stable and install a backports kernel and backports Mesa, which are both currently versions that should support RDNA4 GPUs like OPs just fine. This involves two simple steps after installing:
- Enable the Debian Backports Repo (see https://backports.debian.org/Instructions/). It’s like, one file.
- Install the packages with something like
sudo apt install -t bookworm-backports linux-image-amd64 mesa-va-drivers
and reboot.
Before you take these steps, you probably won’t have hardware acceleration, but will still get video output so you can perform the steps and reboot.
This is definitely a weird suggestion, and other people’s suggestions might be less work out of the box. I just like Debian, and stability+backports+testing is part of what makes it possible for it to be my everything distro.