I find that the Debian/Ubuntu repos (the dpkg/APT system that uses .deb files) have more stuff in them than Fedora’s repos (the DNF package manager that uses .rpm files) do.

Ah, makes sense. That's probably because Fedora doesn't package non-FOSS packages, so you need to use something separate like RPMFusion, and that doesn't contain everything. There's usually a repo for what you want, but for something really niche, yeah, Ubuntu will probably have a better chance of having it, followed by Debian.

That said, I really like the way openSUSE does it. Basically, they have OBS, which is kind of like the AUR, but it actually builds packages for you. I think that's a much better way to handle it than building stuff from source on your local machine, since it allows you to share that package (i.e. dev machine vs other machines you have) and at least track down the dependencies needed since it starts w/ a blank slate. I don't know if Fedora has something similar, and it's certainly not a beginner-friendly option (if you're pulling packages from OBS, you're probably doing it wrong and will likely run into issues). However, that is the first step to getting something included in the official repos.

But if it's not in the default repositories, you should definitely talk to someone more familiar w/ the distro to figure out the "right way" to do it. I've built .debs and AUR PKGBUILDs, but only after learning from the community the right way to do it to make sure it doesn't break on an update. New users are unlikely to put in that legwork, hence the recommendation to never use anything outside the default repos w/o asking for help.

There’s problems at the bleeding edge, but there’s problems at the trailing edge as well.

I agree. I guess my point is that if things work w/ an older set of packages, the chance that things will break is incredibly low. Whereas if things work on a bleeding edge distro, there's a good chance you'll see some breakage.

For example, openSUSE Tumbleweed is generally a good distro, but there was a week or so where my HDMI port didn't work, my default sound device changed suddenly and was no longer consistent (sometimes would pick one monitor's speakers instead of the other, depending on which came online first), and I was stuck on an older kernel for a couple weeks due to some kind of intermittent crashing. This experience was way better than what I had on Arch, and fortunately TW has been uneventful for 2-3 years now (probably because my hardware hasn't changed).

So for a new user, I recommend finding the oldest distro that supports all the hardware you need. For experienced users, I recommend using a rolling, bleeding-edge distro and reporting bugs upstream as they happen, because the frustration of something breaking randomly is much less than the frustration of multilple things breaking on a release upgrade, and it's nice to have the latest improvements to performance and whatnot (i.e. I used Wayland on TW way before it landed on any release-based distro, which was awesome since it allowed me to use different refresh rates on each monitor).

For your example, I'd recommend users hop distros until they find one where everything works. If Mint is too old, try Fedora. There's usually a sweet spot where everything works and you have a reasonably stable experience overall. Even Debian Testing (pinned to the release name, not "testing") is probably a better fit than Arch or openSUSE Tumbleweed.