> Run that on someone else's managed k8s setup ... this way I'm only responsible for my application and its interface.
It's the eternal trade-off of security vs. convenience. The downside of this approach is that if there is a vulnerability, you will need to wait on someone else to get the fix out. Probably fine nearly always, but you are giving up some flexibility.
Another way to get a reasonable handle on the "managing a whole OS ..." complexity is to use some tools that make it easier for you, even if it's still "manually" done.
Personally, I like FreeBSD + ZFS-on-root, which gives "boot environments"[1], which lets you do OS upgrades worry-free, since you can always rollback to the old working BE.
But also I'm just an old fart who runs stuff on bare metal in my basement and hasn't gotten into k8s, so YMMV (:
[1] eg: https://vermaden.wordpress.com/2021/02/23/upgrade-freebsd-wi... (though I do note that BEs can be accomplished without ZFS, just not quite as featureful. See: https://forums.freebsd.org/threads/ufs-boot-environments.796...)