Is there a max number of sessions a single retrieval user license it allotted?

Outside concurrent licensing cases like WebLink, a single user can only have 4 open connections to the Laserfiche repository.

I know in the case of using the Web Client, if the user opens another tab accessing the repository that is counted as another instance.

In general, this is not accurate. The web client doesn't keep track of the number of tabs a user has open, and doesn't know if requests are coming from a new tab or not. If the web client is able to associate the web requests with an existing active session, it won't attempt to create a new one (which is the operation that can fail due to hitting a limit).

What can happen is that a user logs in to the web client and closes the browser without logging out. If they then open the browser again, this will be a new session and will require logging in to the Laserfiche server. This is because the cookie used to associate the user with their sessions was discarded by the browser when it was closed. The abandoned sessions will eventually time out, but the user may get into a situation where all 4 sessions are used up but haven't yet timed out.