Migrate them to a modern filesystem, presumably. ext4 is extremely reliable, btrfs is less proven but much more featureful with copy-on-write and snapshots.
This isn't any type of surprise, ResierFS was marked obsolete some time ago now.
Use a kernel version that still has support to perform the copy before upgrading? If already upgraded, boot to the old kernel? Boot from a live iso that has support?
I mean, this isn't exactly a hard problem to solve...
Use an old kernel version (if yours doesn't still support it) and something like btrfs-convert to get a maintained filesystem instead. Works pretty well in my experience with converting other filesystems to btrfs.
I agree with the other commenter recommending to migrate as soon as possible while the kernel still does support, but that does seem like a workable strategy if you can't for the foreseeable future.