10.15.7 ongoing issues

Usually the first questions asked when Macs are experiencing symptoms like this are:

Do you have any "cleaner" third party software installed?

Do you have any security third party software installed?

Do you have any third party anti-virus software installed?

It seems that the answer is "yes" to all three. Any of these could be interfering with normal MacOS operations. You have a new Mac that should be extremely fast and responsive. I would remove ALL of the above items (completely uninstall them).

Also, you have Profiles (your can see these in System Preferences), perhaps JAMF but maybe others. Sometimes malware installs these and that can slow the computer, or legitimate Profiles can interfere because they can be intrusive. Do you have to use JAMF and those Profiles? You have also disabled the MacOS built in security/protection which means you could have malware. You might consider downloading the free Malwarebytes to do a scan of your Mac for malware.

You also have WD third party disk utility/helper extensions and software installed, it may be trying to interact with your external drive and interrupting processes on the Mac.

I don't recognize a number of your third party extensions, not sure why they are needed. Of course you should be able to install things, but if you have many items running in the background, one wants to be sure that they are needed and useful. Sometimes they can slow down a MAc.

So your employer requires JAMF and Sophos. Fair enough, it's their computer, after all. The MacBook Pro that my employer provides also has JAMF plus a Symantec suite. However, they do extensive testing before installing and rolling new things out so the Macs with their standard configuration generally run smoothly. Although I would prefer none of those Profiles and no Symantec, but like you, don't have a choice.

Does your IT Department extensive test their configurations? If they do, you need to look carefully at anything you have independently installed. Also, if you are able, can you create a new user and log in as the new user and see if the problems are gone? That would make it easier to track down since it would be isolated to just your original account, versus a system wide issue.

Unfortunately, with a configured system like you have, it is best to minimize any customization you might want to do because those things can easily conflict with the sometimes intrusive system changes done via the Profiles and security suites, while on a "clean" Mac they would cause no such problems! I don't do ANY customization on my employer's computer, I only install stand alone programs such as SuperDuper.

Removing software you installed yourself can be challenging, everything must be uninstalled/removed, including associated Startup files, login items, and other things that create background processes. Look for complete uninstaller from the vendor or from other web sites where people have reported success in removal.

Can you change the Sophos system preferences, say perhaps to not do constant monitoring but instead to just do daily scans, for instance, something less intrusive?

Something that interferes with MS-Word or Apple Music is being pretty intrusive and the forced shutdowns seem to indicate something very basic is amiss. It could be an endless detective hunt on a computer that you can't even configure yourself. I would try to make it as clean as possible with only the employer-mandated stuff on it, to start, and then slowly install only things you REALLY want to have and retest after each install.

Read the document below and especially the part about using Time Machine with NAS

Backup disks you can use with Time Machine