Hey z3bra no offence but rsync combined with borg/bup is imo in most cases a more suitable solution than a logrotate on that file.
While yours seem to be good enough for simple config files that can be easily backed up, it fails with massive data like my video or audio list.
(I do also understand it's just a pointer into the right direction)

Right now I am looking for a good combination of a backup where I can go back in time and have checksums and incremental snapshots, like a mix between rsync and bup (or borg). Borg seems to handle it all very well and is tested against 10TB and more storage, I however didn't get fully convinced yet so I am still looking for alternatives. (I dont like that everything is included and you have to write an excessive list of excludes or let it be generated via a find-command)

I will give your "synk" a look and may report back for duty.