Define "the OS package manager". If the distro comes with flatpack and dnf equally, and both are invoked by the generic "get updates" tooling, then both could count as "the" update manager. They both check all apps for updates.

Odd to advocate for docker containers, they always have the app provider also on the hook for all dependencies because they always are inherently bundled. If a library has a critical bug fix, then your docker like containers will be stuck without the fix until the app provider gets around to fixing it, and app providers are highly unreliable on docker hub. Besides, update discipline among docker/podman users is generally atrocious, and given the relatively tedious nature of following updates with that ecosystem, I am not surprised. Even best case, docker style uses more disk space and more memory than any other option, apart from VM.

With respect to never having to worry about bundled dependencies with rpm/deb, third party packages bundle or statically link all the time. If they don't, then they sometimes overwrite the OS provided dependency with an incompatible one that breaks OS packages, if the dependency is obscure enough for them not to notice other usage.