I just hate that while the [Time Machine] GUI is displayed, I cannot do anything else.
This is by design.
The Time Machine (henceforth referred to as TM) UI is very specific; unlike any other application from Apple, it literally takes over your entire desktop and forces you to focus on it because it needs your undivided attention.
Backing up files is actually pretty easy. You simply make a copy of the file and archive it so that in the unfortunate event something goes sideways, you have a recent copy of the file from which to restore.
In fact, Time Machine is operating, in the background, continually taking snapshots ever hour
When you use Time Machine, Time Machine also saves local snapshots you can use to recover previous versions of files, even if your backup disk is not attached. These snapshots are created hourly…
First, this “hourly” snapshot is not “every hour on the hour.” It is roughly every 60 minutes or more accurately, every 3600 seconds give-or-take a predetermined fudge factor. Secondly, while TM is making periodic snapshots, it can do so in the background because this is not an activity that will impact the system in any way.
Restoring files is the critical activity
Whether on your desktop or in the datacenter, when files are being restored, writing of new files is stopped. The reason for this is to avoid version conflicts. TM cannot “know” what you intend to recover even if you yourself are very clear on it.
TM needs to stop taking snapshots and/or making its backups, allow you to restore what you need and when you’re finished, it will begin making backups of those new files as you work.
No, you cannot minimize, “window”, move to a Space the Time Machine User Interface. It is by design that when restoring files, it requires your undivided attention because it needs to pause its activities so that you can effectuate a restoration of file(s).