Catalina - Data Folder

In principle, you should be able to create that folder inside the Users folder. It is quite normal that you are asked to authenticate, because you are not the owner of the Users folder.

Why would you not want to use the normal Documents folder inside your own home folder? Care to explain?

In previous macOS versions, I used to have my main Documents folder at the Root of my mac (Macintosh HD/Documents) sitting beside the Applications, Library and System folders.

Understandable, but in Apple's effort to protect macOS (in addition to protecting users from themselves and other users) that technique won't work in recent macOS versions. Don't become distracted with the creation of "Macintosh HD - Data". Neither one's root level should be used, so the fact Catalina bifurcated the startup disk is not relevant to that particular concern.

Will every time I create a library for an application or try to read/write to that location, will there be permission problems?

Probably.

As this is no longer possible, I was wandering if anyone had any information as to which parts of the Mac I can safely create my master Documents folder to.

Generally speaking the Home folder is where all of its User Account contents should reside. That's your playground, within which you can do whatever you want. Other folders have restrictions.

Home includes Documents and others Apple helpfully provides. Their contents are restricted to that User Account. If you want to share files (for your proposed "master Documents" perhaps??) use the Shared folder. It's available to all users of that Mac.

I think that's what you'll want to do in lieu of a Documents folder at the root level of its startup disk as you had been accustomed to doing.

Review Folders that come with your Mac - Apple Support.