Huh? You're saying there is some sort of "safety mechanism" to prevent making the iPad incompatible with your computer's OS? Or does that apply only from now on (after iOS 13.x has been installed)?
No, the opposite if anything -- once the iPad is running iOS 13, you're locked into needing El Capitan or higher on the Mac in order to sync with the iPad, regardless of which iTunes version you run! I'll try to explain again, hopefully more clearly this time.
Starting around iOS 12.3, Apple stopped updating iTunes directly and instead started releasing updates to
portions of macOS that are used by iTunes to sync with iPhones and iPads. Apple released these updates for El Capitan and later, but not Yosemite or earlier.
Once the iPad is running iOS 13.x, the
Mac needs to be upgraded to El Capitan, so that the
Mac can get the
OS X/macOS update for iOS 13 sync compatibility that applies on top of El Capitan (or Sierra/High Sierra/Mojave). To put it in other words, Apple is updating macOS instead of updating iTunes, so that the old iTunes will work with the new iOS without actually updating iTunes itself, and you need to be running at least El Capitan in order to install these macOS updates.
I hope this is clear now. (One extra wrinkle: The iOS 13 compatibility update does not actually show up in the App Store or Software Update. Rather, you must first plug an iOS 13 device into the Mac that's running El Capitan. Then a dialog box pops up asking if you want to install the update, and if you agree, then the Mac downloads and installs the update. That's what I was trying to explain in the part of my post that you quoted.)
Regarding downgrading iOS: It's theoretically possible on devices with an A11 CPU or older, but the 5th generation iPad Mini has an A12 CPU. When the A5 CPU came out in 2011 and fixed the A4 CPU's boot ROM flaws, it took until 2019 for someone to find a boot ROM flaw in the A5. Now that the A12 has fixed the boot ROM flaws of the A5-A11, it'll probably take years (maybe almost another decade again) for someone to find another boot ROM flaw that would allow a downgrade.
Incidentally, there are some other downgrade methods that don't rely on boot ROM flaws -- for instance, it's possible to downgrade some iPad 2's to iOS 6.1.3 or 8.4.1, but that's only possible as a side effect of the fact that over-the-air upgrades of an iPad 2 from iOS 5.x to 9.3.x require going through 6.1.3 and 8.4.1 as intermediate steps. This type of downgrade method
never allows downgrades to the version of iOS that first shipped with that model.