Can Time Machine back up all 4 of my internal drives (Mac Pro 5.1) to one backup drive or RAID system, assuming enough capacity? (8TB to back up)

For long-term trouble-free operation, the recommended size of the backup drive is at least 2.5 times the total of what need to be backed up. (There are some diabolical situations you can get into when you need to make a complete new copy without discarding any of the old.) You CAN use a drive that is smaller, but you will get into trouble sooner. Better to start NOW with a drive too small than none at all.

You can create such an enormous drive using one very large drive, -OR- you can create a trivial variant of a RAID set called a "concatenated RAID set" which, as it sounds, is just a bunch of drives pasted together through software to act as one.

Time machine will typically back up all your local drives, but you can check the settings to include or exclude anything you care to. Time Machine BACKUP is built into MacOS, so that it has the permissions need to access everything and back it all up. Its settings are controlled by System Preferences > Time Machine. The (Options) button give access to the Include/Exclude list.

The locations, ownerships, and permissions of every file are meticulously maintained throughout the entire backup and restore process.

Restore is handled with an Application, Time machine.app

Back up your Mac with Time Machine - Apple Support

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If you buy one, a drive 2 to 3 times or larger than your boot drive is preferable for long term trouble-free operation. Do not pay extra for a drive that is fast.  (You can get by for a while with a "found" smaller drive if necessary, but it will eventually become annoying).

Attach your external drive and use

System preferences > Time machine ...

... to turn on Time Machine and specify what drive to store your Backups on.  It may ask to initialize the new drive, and that is as expected.

Time Machine may spend all afternoon making your first full backup. You can continue to do your regular work while it does this. The first Full Backup is by far the biggest backup. After that, it will work quietly and automatically in the background, without interrupting your regular work, and only save the incremental changes.

Time Machine's "claim to fame" is that it is the backup that gets done, because it does not ruin performance of the rest of the computer while doing its backup operations. You do not have to set aside a "Special Time" when you only do backups. When you need it, your Time machine Backup is much more likely to be there.

If you choose to connect your Time Machine backup drive only from time-to-time, try to do so at least every-other day, at minimum. Otherwise, it may take several hours of computation just to decide what needs to be backed up, before any files are transferred.

A Network Attached Storage device is a computer with a minimal Operating system already set up just to act as a smart drive on your network. It usually includes some version of Linux, because it can do the job and is cheap to implement.

But the added expense on a NAS is not necessary for this purpose. A simple large slow drive or concatenated RAID will do fine, with out the added cost or added complexity. MacOS has all the software needed to make a concatenated RAID for you out of several drives. In recent versions of Disk Utility, it is a choice on a menu, sort of "put away" so that novice users will not stumble upon it and hurt themselves.