Recently when I was using Google Photos it’s always stuck on “preparing Backup”. I did the following things and the backup started then. Not sure what step(s) is(are) the key to solve the issue, but record them here:
Go to “Settings” to enable the “Background App Refreshing” for this app.
Open the app, check the photos which are NOT be uploaded, open some of them can tap upload manually.
Check the videos which are not uploaded and do the same thing as step 2.
After that the app started the upload process. Some other tricks such as “enable cellular backup” mentioned here may also work.