How can I rearrange photos within a shared album?

What system are you running?

Are you referring to the order in your Shared Albums in your Photos library or the online shared album?

With Monterey the user can sort a local shared album ( in the library) as shown in this screenshot:

Manually sorting is not an option.

The online shared album is only displayed in the order they were added to the album.

Would be great to be able to define the sort order e.g. as part of the shared folder properties. Thanks