Photos library permanently remove from time capsule

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I'm having trouble knowing what the screenshot you've posted means. Are these items that were backed up by Time Machine or by you manually adding them to the Time Machine drive? If the library that's shown was backed up by Time Machine and not added by you manually you'll have to enter Time Machine via it's menu bar menu

locate the latest occurrence of the Photos library, Control (right) - click on it and select "Delete All Backups of Photos.photoslibrary".

Note this will delete ALL backups of the Photos Library from the TM backup drive.

After clicking OK you can click on the Cancel button in them main window to exit Time Machine. It will take a while to finish the job.

Keep the TimeCapsule connected to USB, then check the permissions on the Photos Library as described in the error message you are seeing: "The operation can’t be completed because some items had to be skipped. For each item, choose File > Get Info, make sure ‘Locked’ is unselected, and then check the Sharing & Permissions section. When you are sure the items are unlocked and not designated as Read Only or No Access, try again."

Select the library on the Time Capsule, and use "File > Get Info". ensure, that the lock is not set, then give yourself Read&Write permissions.

As you only want to delete the Photos Library on the Time Capsule, you can look inside the library package and unlock and delete the items inside individually. Ctrl-click the Photos Library, then use the command "Show Package Contents".

Now open the Info for each item and subfolder and unlock it individually. After changing the permissions for a subfolder click the gears icon and use the command "Apply to enclosed items".

Then try to delete each subfolder individually, if you still cannot delete the library as an entity.

It might be a problem of the network connection on macOS 10.15.6 Catalina. Try to use a wired connection for your Time Capsule, then try again.