I have a MBP 2014 and MBP 2019 with both running Catalina.
Recently, the MBP 2014 received an update for the OS and I clicked on it.
After the download, when installing the update, it came up with the low disk place error.
When I first installed on my MBP 2014, i do get that message and was able to clear out some disk space.
Was successful in installing Catalina and using it.
This update in return doesn't allow me to free up my disk.

I'm trying to recover my data from the MBP 2014.
Connected both machines with Thunderbolt cable and turn on my MBP 2014 under Target Disk Mode.
On my MBP 2019, I'm able to see macintosh HD and macintosh HD - Data in disk utility.
However, there is only macintosh HD in Finder.
When I click on it, I'm unable to see my account folder (username) under Users folder.

Appreciate if fellow members could advice if I've have tried this the wrong way and how can i access to my data on the MBP 2014.

Why no backup?
Why low disk space still perform MacOS upgrade?

All that aside.

You might want to try login as root user and see the "data" volume show up. It might be hidden or unmounted due to MacOS upgrade progress & permission issue. Try terminal command and check your "data" volume still exist, "diskutil list".

You might also try do a search for the user folder in finder. MacOS installer will move or archive the user data during installation.