Create a new record - what do you see by way of confirmation when completed?
The add new user button should be a plus in the header of the results list, like in user permissions. That means one will be viewing the user profile as soon as one clicks "+".

Displaying lists within a record
Is there plenty of real-estate for multiple columns?
On large displays there should be — additional features like maximizing the preview pane; or maximizing a list component will provide extra real estate (see diagrams attached)

You may want to be able to search/filter these lists in some cases
Each column header works as a filter field – click and type to filter that pane

You may want to be able to link to (or otherwise access view/edit) the records in these lists
That content should open as overlays or modals... see answer below.

Linking directly to individual records (via direct link or from elsewhere in FOLIO)
If we had a notion of Content Types, or if each app could serve a stand-alone display of a piece of content, that content could be opened within another app. E.g. one would be able to open a patron inside another app, hence not interrupting any existing flow in the Users app. Alternatively an overlay could be opened inside the Users app. Another option to explore is having a tab-like functionality within each app — this seems to have many technical implications, though, and one might argue it is recreating the functionality the browser provides (though not all client browsers would have tab functionality easily available / available at all, so I would disagree with that opinion).

What displays in Search/Filter pane?
Depends on the direction chosen from the ones above

What displays in Search Results?
Depends on the direction chosen from the ones above

What is expected when you click the back button?
Refer to discussion previously had.

Let's make sure we consider the two different screens we currently have to edit records (actually, it would be good to consider whether they could be consolidated - I'm not saying they have to be, but let's see if there's a way, as it would reduce complexity)
I agree — see above description of adding a new patron