cannot start editing photos

As a test launch Photos with the Option key held down and create a new, test library.  Import some photos and test to see if the same problem persists. Does it? (This tells us if the problem is limited to your current library or is more wide spread)

If the problem persists boot into Safe Mode (Use Safe Mode to isolate issues with your Mac and Playing Safe: what does Safe Mode Do?) and check there to see if the problem persists. (This tells us if there's any 3rd party software that might be contributing to the problem).

NOTE: Safe Mode boot can take up to 10 minutes as it's doing some system cache cleaning, volume verifying and directory repairing. 

Also what system and Photos versions are you running? Where is your library located and if on an EHD how is that EHD formatted and connected to your Mac?

Now that the test library works OK try again in your original library. That often fixes preference and cache files so the original library will work.

If you still can't edit in the original library log into another user account, Set up users, guests, and groups on Mac,  repeat the test library see if the problem persists. (This tells us if the problem is limited to your user account or is system wide).

If you can edit in the other user account go back to your account and download and run Etrecheck. Etrecheck is a diagnostic tool that was developed by one of the most respected users here in the ASC and recommended by Apple Support  to provide a snapshot of the system and help identify the more obvious culprits that can adversely affect a Mac's performance.

Copy the report

and use the Add Text button to include the report in your reply. How to use the Add Text Feature When Posting Large Amounts of Text, i.e. an Etrecheck Report

IMPORTANT:

Before running Etrecheck assign Full Disk Access to Etrecheck so that it can get additional information from the Console and log files for the report:

ALSO IMPORTANT:

Then we can examine the report and see if we can determine the root of the problem.

Try selecting the Photos library package and bring up the Info pane.

In the pane go to the Permissions and Ownership section and set Read and Write to you, everyone, the group that's there and admin. If no admin is present add it.

Open the library and see if you can edit older photos.

Since you can edit in another library in your user account and in a library in another user account it appears that your library is the culprit.

I would suggest that you run the Photos first aid on the library but it can have some adverse effects on the library, like removing all of the face recognition from it. Léonie knows more about that and I'll set her either confirm repairing the library or not. Whatever you do make sure you have a current and full backup.

Then I would test with one photo, that cannot be edited, can be reverted to the original.

That requires however, to get into the Edit mode. Are you seeing the error message, as soon, as you click the Edit button? Or can you at lest get into Edit mode, so you can click "Revert to Original"?

If you install PowerPhotos (the free trial version will suffice) and it can open the Photos Library, you can see the path to the original image file in the Info for selected photos.

You can download PowerPhotos here: https://www.fatcatsoftware.com/powerphotos/Docs/merge_libraries.html

Then you can compare the original image files and check them in another application, for example Preview. The Inspector in Preview can show you all kinds of EXIF and IPTC tags.

Did you install the update to macOS 10.15.4, and if yes, and did it make any difference?

Are you running a managed or referenced library?

Do you have iCloud Library enabled and, if so, is "Optimize Mac Storage" selected?

Also did you try another test library as I suggested and in another user account?

What is the source of the photos? Have the photos been taken or edited with an iPhone or iPad, perhaps with an earlier version of iOS? Or have the photos been migrated from an iPhoto or Aperture Library? It may not be possible to edit a photo, if it has been edited in Aperture or iPhoto, unless we revert the photo to the original. The same may happen, if a photo with adjustments or effects applied has been synced from an older version of Photos iOS.

Is there any chnace that the library might be damaged? Has it been restored from a backup? Or synced with iCloud Photos with devices using differnet system versions?