I can imagine a huge number of properties.

1. Eventual consistency: if no new edits are generated, then eventually all connected viewers see the same document.

2. Durability: if the system acknowledges an edit, then that edit is stored permanently in the undo/redo chain of a document.

3. Causal consistency: if the system acknowledges an edit B that depends (for some definition of depend) on edit A, then it must have acknowledged A (instead of e.g. throwing away A due to a conflict and then acknowledging B).

4. Eventual connection: if, after a certain point, the user never fails any part of the handshake process, eventually the user can successfully connect to the document (there are definitely bugs in collaborative tools where users end up never able to connect to a document even with no problems in the connection)

5. Connection is idempotent: Connecting once vs connecting n times has the same result (ensuring e.g. that the process of connecting doesn't corrupt the document)

6. Security properties hold: any user who doesn't have the permissions to view a document is always denied access to the document (because there are sometimes security bugs where an unforeseen set of steps can actually lead to viewing the doc)

6. Order preservation of edits: for any user, even a user with intermittent connection problems, the document they see always has an ordered subset of the edits that user has made (i.e. the user never sees their edits applied out of order)

7. Data structure invariants hold: these documents are ultimately backed by data structures, sometimes complex ones that require certain balancing properties to be true. Make sure that those hold under all edits of the document.

Etc. There's probably dozens of properties at least you could write and check even for an abstract Google Doc-like system (to say nothing of the particulars of a specific implementation). That's not to say you have to write or verify all of these properties! Even just choosing one or two can give a huge boost in reliability confidence.