For the last question, Ideally, the L4 schedule should be a more detailed breakdown of the L3 schedule. It should contain activities that are directly related to and support the L3 activities.
This hierarchical structure allows for a better view of the work while still linking back to the higher-level objectives of the project.
So, both L4 and L3 schedules should be based on the same WBS hierarchy and complete each other, unless there is another agreement on an update.
At the moment I think that you have to focus on the L4 schedule and make sure it mirrors the projects and represents the WBSs clearly and take it as a starting point.
For the second part of the question on how to monitor the project while not respecting the baseline, The answer is really simple.
When we think of the word “monitor” or “control” and understand their meaning, you’ll find that you cant monitor something or control it to know if it’s doing good or bad without having a reference.
So, you must have a reference to measure the progress from, to know if you’re going ahead or going backward.
As you don’t respect the baseline, you have to ask the client with an official document to create a recovery schedule and submit it to you for approval.
Then you can study it and make sure it represents the current status, then start collecting updates from the site and auditing it and monitor the project from a good starting point.