I found and fixed it, as it seems.
My 3 databases are encrypted on DEVONthink, which means that their size is restricted on Mac.
One of them got fill up too much from an iPad, which does not have that restriction. So, the remote sync location was too large for DEVONthink on Mac.
I think this corrupted the datbase and somehow this got mirrored back to the sync location and from there back to the iDevices.
I deleted the iPad, made a new and larger encrypted database on DEVONthink and moved the olde4 content from the bad into the new encrypted database.
Then I synced this back to the remote location, deleted DTTG from an iPad and one by one added all databases back, inbetween testing if searching for tags works again.
It seems to be OK now.
I only need to repeat on the other iDevices.
Encrypted databases that are too small for a remote sync location seem to be a source of corruption!