How do you move an Album from a shared library to your personal library?

No. Albums always stay in your personal library; only the photos and videos "move" between personal and shared libraries. Luckily, selecting all of the contents of an album is as easy as entering the album and issuing select-all (command-A).

What I am doing when sharing photos in the Shared Library I am adding the name of the album as a keyword. The recipients can easily recreate the albums with a smart album "Keyword is ...".

The name "Shared Library" is a bit misleading. We can only share the media inside the library, but not the structure. And what is a library without its organisation?

Let's say I have family photos from the past 30 years and I want to share those photos with my mother. The way you've described this implies that I have to have my mother organize tens of thousands of photos she didn't take into galleries and folders, even though I have already done all of that work. That requires the shared party to be both computer savvy and a heavy Photos user. What would be more useful for my use case is the ability to share galleries and folders and have those show up with the same organization and structure in her Photos app. I want her to be a consumer of the existing structure rather than a creator of a new structure based on my going through each album and adding metadata to the pictures to name the album and have her pull that specific metadata and create new albums on her own. That will likely never happen, but she would happily view something that I've already done.

Way back in the iPhotos days, I could share albums via a website (sort of like Flickr) where they can see multiple albums and navigate from there. That functionality was replaced with the current sharing options, but that doesn't present a site with multiple galleries that someone could navigate. I eventually started uploading pics to Flickr, but even that is a lot of manual work because there wasn't functionality to easily convert albums in Photos to albums in Flickr (you have to manually export the photos in an album, upload that folder to Flickr, and then organize those photos in Flickr into albums which is essentially duplicate work like the current shared photos feature).

So in conclusion, it would be lovely if there were an enhancement to the shared library to allow the sharing of entire folders and albums (not just photos within an album) with their existing structure for other Photos users, and an Apple version of a Flickr-type website where you could share a set of public galleries that are navigable from a public shared album home page for non-Photos users and Windows folk.

Thanks for your time if you made it through this response! lol

How are the photos organized if you remove them from the albums and groups on my personal library? If I want to move 30,000 photos to a shared library, it does me no good to move them into a single big pool. You lose all of the organization and make any shared user less likely to be able to find things. Am I missing something?

The photos remain organized for you when you view them with your personal library open. Apparently other subscribers are responsible for imposing whatever Folder/Album structure they want to see.

The attributes that are stored with the individual photos are visible to any subscriber. Last I tested, those included keywords, locations, descriptions, captions, and titles. Some of them can be used by other subscribers to construct Smart Albums.

Let's say I have family photos from the past 30 years and I want to share those photos with my mother. The way you've described this functionality implies that I have to have my elderly mother organize tens of thousands of photos she didn't take into meaningful galleries and folders, even though I have already done all of that work. That makes the feature not useful for someone who isn't both computer savvy and a heavy Photos user. What would be more useful for my use case is the ability to share galleries and folders and have those show up with the same organization and structure.

I think you have a point, but I only get to describe what Apple has actually provided. If you want to suggest to Apple that they provide additional features, you can use their official feedback pathways.