I found out Restic cannot handle files changing during a backup and found BTRFS/ZFS snapshots as a possible solution (see How does Restic manage changing files during backups? and Creating BTRFS snapshot before runnning restic backup). The issue is that the OS I am running does not support either of these out of the box and instead uses the XFS filesystem. I would prefer to avoid migrating to a different OS just because of this.
What are users running non-BTRFS/ZFS filesystems supposed to do?
if for whatever reason it is not possible then you can always create local copy of your frequently changing data and backup from there. Maybe not very elegant and efficient but for sure working solution.
Overall it is your responsibility to provide restic with stable data source.
And good learning that when choosing filesystem for your distro, backup requirements should be taken into account from the start.