P: Edit/Sync Photo changes the Capture Time.

Having the same problem - changing develop settings or flags seems to trigger the change for individual files.

New info: Globally pausing syncing stops it, but turning off sync for the only collection containing the files I'm working on DOES NOT stop it. When I look at sync status, it periodically shows that a dozen or so files from the collection are being synced with metadata or data upload, despite the fact that the only collection containing those files is marked as "don't sync".  

New info: I uninstalled the 14.1 and re-installed 14.0.1 (preserving preferences). As soon as I un-paused syncing in 14.0.1, it showed "migrating sync data" for a minute or two, then resumed the behavior - it started syncing the problem files even though the only collection they're in is marked "not synced", and changing the capture time as it did so.

As far as I am concerned I did not downgrade. I can fullfill the photo report I am working on without it being sync to the cloud so I just paused the sync for now.

It could be.
However in this case it is very likely that people who downgraded to 14.0.1 would still be facing the issue and it seems they do not experience the problem anylonger.

I think that the conclusion that this is a bug in the 14.1 application, and so downgrading to 14.0.1 is the solution, is premature. This could also be a bug in the server software, that just happened to occur around the same time that Lightroom Classic was updated to 14.1.

I actually went back to LrC 14.0.1 and at least Cloud Sync was no longer proactively changing the capture dates of my files. So I went ahead and (AGAIN!) manually corrected capture dates of all affected files. Then I realized that the changed capture dates were NOT synced back to LR cloud (i.e. for the same image, I saw different capture dates on LrC desktop and the iPhone that syncs to LR cloud). I then tried to change those files on my iPhone (where the capture date was still wrong) and again that wrong capture date was synchronized back to LrC desktop (it seems like the cloud is synchronizing with LrC desktop, but not the other way around ... at least not when it comes to capture date). I then corrected those files again in LrC desktop and forced LrC to write the metadata into the file (or sidecar file). Then (finally) it started syncing correctly back to the cloud.

Tl;dr: I rolled back to LrC 14.0.1, corrected all affected files (with wrong capture date) in LrC, and forced LrC to write the updated metadata to the files. That did the trick for me. I'll keep investigating what's going on and report back if I find anything new. But at least for now, I'll certainly stick with LrC 14.0.1.     

Interim solution: change back to LRc 14.0.1 select photos which have wrong date and time. Then go to Metadata; change to original capture time. Then all is set correct again. Wait for a bugfix from Adobe. 

Same, Lr has no involvement in my editing process, I don't even have it installed. All photos were imported directly into LrC and edited either in LrC or Ps. This issue only appeared once I was done editing and synced the collection they were in to the cloud.

Several users stated that the time shift occured several time (probably at each sync) and that made theses pictures timestamp go back to several days, weeks or even months. It is likely what happened in your case

I am pretty sure that the pictures I have the problem with were neither imported or edited in LR. They went the full way from importation to problem occuring on LRC.
As stated earlier the problem seems to be on the sync process

.... one other thing. LR does not change to a definite time (eg from capturing to editing). I have images changes to a month ago.  Very strange error.