On Synology, the only sensible way to use Syncthing is to check that option to ignore permissions. In fact, I added it as a default to the most recent package release on SynoCommunity. But unfortunately that only applies for new folders created after a fresh installation, so might not have helped in your case.
Go ahead and check that option for every existing folder on the NAS, and ideally also on folder defaults so you won’t need to remember it in the future.