What will happen if I interrupt Time Machine clean up?

TM is busy deleting old and "expired" backups in anticipation of the next incremental backup.

That's also the reason it takes people by surprise when they see so much empty space after a backup finishes. They didn't see how much was left in the interim. TM never deletes old, "expired" backups until after it finishes a newer one, thus ensuring you always have at least one at any given time. For at least a little while, your TM backup disk will require twice as much space as the source volume's contents — plus an additional amount for temporary storage.

It is taking a long time because of the enormous number of files that need to be backed up subsequent to upgrading macOS. It's ok to interrupt it.

The backup won't fail. It's already finished. TM is extremely conservative in that regard. It's designed to cope with all sorts of interruptions. You can (and probably should) completely ignore it.

Subsequent backups won't take as long, although I have observed sometimes it takes two or three backups before it eventually settles down. The "cleaning up" stage will just take as long as it needs. And, depending on that Mac's previous macOS version it may also convert the backup disk to APFS, which it also does in the background. That takes a very long time, and again it's best to just ignore it.

If Time Machine takes a long time to back up - Apple Support

gfiedel wrote:

Backing up took 18-19 hours after upgrading to Sonoma. Now, it's cleaning up. If I interrupt clean up will I lose the backup?

I have "interrupted" the "cleaning up" phase of Time Machine many times when in a hurry to shut down my laptop and go somewhere with it and it never has caused me a problem. I have also interrupted Time Machine even WHILE doing a backup, to eject the backup disk or shut down the Mac and it always catches up next time it is connected. The key is to wait to allow the Mac to eject the drive in an orderly way or shut down using its normal process. That usually takes less than 10 or 20 seconds at most.

That's correct. TM has to delete old and expired backups eventually. You can interrupt it without any consequence, and it will just have to pick up where it left off.

gfiedel wrote:

Backing up took 18-19 hours after upgrading to Sonoma. Now, it's cleaning up. If I interrupt clean up will I lose the backup?

Time Machine only works when actives— so it will resume when you stop interrupting...

It's ok to connect your backup drive only once in a while. When recharging the Mac, for example, might be convenient. Time Machine maintains "Local Snapshots" that can be used to completely restore the Mac's content. They are created automatically, and are written to the TM backup drive when it is finally connected. They are overwritten about every 24 hours so that's as far back as you can "restore" from them, should that be required.

About Time Machine local snapshots - Apple Support

"Local Snapshot" limitations involve the storage capacity of the source volume, and the fact they won't be useful if that source volume fails, becomes unbootable, etc.

So, connect the TM backup drive overnight, when recharging, or whenever it's convenient for you. As you found out though, it will begin to complain after ten or more days elapse without connecting a backup drive.

An even better idea is to have two or more of those backup drives, and connect them in rotation.