I ran into a problem I have never seen before —
I lost the sync on my iPhones DTTG installation. iPad and Mac syncs fine, but not to iPhone. I received both of the errors in the images. I had just prior totally reorganized my groups on the Mac build. At the time I was running the most current DTTG beta build on both my iPad and iPhone. But I only have a problem with the iPhone.
Any ideas? I already turned on and off iCloud syncing in both the iPhone and macOS installation and turned it back on. Deleted and reinstalled DTTG.
Have you updated to DEVONthink To Go 2.7.6? If yes, maybe the sync store on iCloud itself is damaged. You could try to verify it from the Mac side and if it is damaged, clean it and re-sync the data.
It works now, it seems, without any additional intervention - it is currently downloading to iPhone.
I had repaired the database and manually re-synced it in the Mac. In addition I created a test database through DTTG (which worked fine). Then after I got your message I went back to DTTG, and despite the triangle warning icon in the top corner still, I went to settings and sync and it refreshed with my Mac database there.
I am sure it was beta related since this is the first month I have used a beta and have had no sync problems in the last two years between macOS and iOS.
All is well now it seems.
It works now, it seems, without any additional intervention - it is currently downloading to iPhone.
Thanks for the follow-up… and ugh! 
But still useful corroborating evidence for us. Cheers! 
