I am experiencing the spotlight indexing stopping Time Machine backups also on external disks connected via USB and formatted as APFS.
I am gonna describe again the behaviour:
1) A Time Machine backup starts (either automatically or manually), NO MATTER if the target is a network volume or an APFS formatted disk connected via USB
2) The backup doesn't complete, it gets to 50%-70% and then gets stopped by Spotlight (clearly stated in console messages: MDSYNC process stops the backup)
3) The cleanup process in Time Machine preference pane seems to go on but its indicator doesn't advance, after a while it seems to finish (I couldn't yet understand if the cleanup has been really done or if that was stopped too)
4) Spotlight starts to re-index the entire backup volume/disk from scratch: A bunch of MDWORKER processes can be seen in Activity Monitor and by checking on their info panel the open files I could see access to the backup volume/disk were made.
Clearly this thing contribute to battery drain especially when the disk is a network volume.
5) Trying to backup to the same volume/disk again right after the pattern just described means going back at square one of this pattern.
Attempts done to mitigate the problem:
1 - Spotlight re-index of the whole internal disk -> didn't solve it.
2 - repair network backup volume via Time Machine menu item option (option-click TM menu item) -> didn't solve it.
3- reapair via diskutility internal disk and backup volume/disks either in recovery mode or while logged-in normally -> didn't solve it.
4 - Ditch TM backup for a new one -> partially mitigated the battery drain since Spotlight won't have to re-index many older backup snapshots. Problem not solved though.
5 - Booting in safe mode and then running the TM backup: backups are done as before the 11.3(.1) update(s), no weirdness with Spotlight re-indexing.
Regarding this last thing and before someone jumps to conclusions about malware or other weirdness:
I don't have any illegitimate daemons or agents in both /Library/LaunchAgents and /Library/LaunchDaemons: iStatMenu, Adobe Creative Cloud, BlockBlock, CarbonCopyCloner, LittleSnitch, Whatroute and Epson software update (should be epsonercp).
All of these updated to the latest versions.
Both /System/Library/LaunchAgents and /System/Library/LaunchDaemons seems legit too, containing only Apple's agents and daemons (plus openssh, apache, etc.).