> It means that somebody must properly recompile, test, fix bugs, integrate, and package the software package into existing distribution.
Recompile, yes. The rest, probably not - upstream usually does that better than any distro. Distro-specific bugs are usually caused by that distro's changes made to "integrate" the package into the distro, which are usually not something the user wants. Again, hence the popularity of PPAs and Snap/FlatPak.
> Fedora often publishes even pre-release versions of some software packages, if you want to talk about "latest" version.
Fedora has the resources to do that because they're managed by a huge company, and they're big enough that upstream will likely make changes to accommodate them. Most distros aren't on that level.