Added new albums, but photos library date has not changed

The date modified of the Photos Library is not regularly updated since Catalina.

The Photos Library is actually a folder, bundled as a package. When Photos modifies the internal files in this package, the modification date of the enclosing folder is currently not always updated. Even the size is not always updated instantly.

But the library seems to be working as expected.

as there is no way of telling as cannot see the contents

Of course you can. You just dragged and dropped it to the external? Then just one it: Hold down the option (or alt) key and launch Photos: From the resulting menu select 'Choose Library'

Photos will remember the last library opened and open it again by default at the next launch. Use the same process to switch back to your previous default library (usually located in the Pictures folder in your user home directory).