Updates, Drives, and Startup. Oh my!

I am trying to confirm all is setup as it should be after the recent 11.3 update.

My main concern is a discrepancy between Live and Recovery modes as well as having the correct startup disk.

This is what I see in Disk Utility while using the live enviroment: I have my system (Macintosh HD Snapshot), my data (Macintosh HD - Data), VM Volume, Preboot Volume, but no Recovery Volume (1 Not Mounted). Notice that only one disk is showing.

This is what I see using Disk utility in Recovery mode. Sorry for the picture quality Recovery doesn’t allow screenshots. Here we see the same disk but this time it is “Container disk3.” Now four volumes are Not Mounted - My Data, Preboot, VM, and Recovery.

We can also now see the macOS Base System disk image which is not visible at all in live mode.

To further concern me Macintosh HD is my only option for a startup disk. I cannot see or select macOS Base System. This should be my startup disk correct?

I will add more in the discussion.