Hi Alan - I might be able to clarify how I fixed the issue of not being able to delete personal snippets but I am not sure what you have tried exactly and what exactly is not working. I see you said you attempted to change the sync from OneDrive to iCloud. There is a notice to check the Sync help page that states essentially (see image for specific wording) Dropbox is preferred and iCloud and GoogleDrive are known to cause problems. For those reasons, I did not choose iCloud nor Google.
If you switch back to OneDrive, I found that the sync folder I had been using in Big Sur still worked on the Mac running Big Sur without any change of configuration needed. The only machine that required me to change the Alfred preferences sync folder location was my Mac running Monterey.
I don't know that the path that worked on my Monterey machine will work for you but my guess is you could probably get on the right path using the information above. I just used Finder to find the folder location by navigating down to the root of the hard drive and then clicked on "Users" --> my username --> "Library" --> "Group Containers". At that point you should look for the folder with ".OneDriveSyncClientSuite" in it (maybe that folder will start with "UBF" but if it doesn't...). Once you find that then click on "OneDrive.noindex" --> "OneDrive". Then continue clicking on folders until you get to the location where your Alfred preferences folder is located.