Can older Mac Pro towers be upgraded?

Simple answer, no, a 2012 Mac Pro cannot be upgraded to the latest version of macOS by any means. And yes, it’s a hardware limitation.

Latest maximum macOS supported: macOS 10.14.6 (18G95) (Mojave) with recommended Metal-capable graphics cards.

Depending on the exact model year of the Mac Pro will be what you can upgrade to. Yes. this is limited by hardware. Basically CPU and Video Card.

2010 and 2012 models can upgrade up to Mojave (4 versions back from current) if you first upgrade the Video Card to a Metal Capable replacement: link ➡️ Install macOS 10.14 Mojave on Mac Pro (Mid 2010) and Mac Pro (Mid 2012) - Apple Support

A 2013 black trashcan model can update to Monterey.

If you don't need the Mac Pro to browse the web and run modern Applications a. 2012 model will o.k. if you need modern versions of apps then it won't run them anymore and will be stuck with older versions.

A 2013 model will still be usable today however even though it cannot update to Ventura, and will be stuck at macOS Monterey. One version back from current.

link ➡️ Identify your Mac Pro model - Apple Support

The Mac Pro 2012 can be hacked a little, but can not run the latest MacOS Ventura no matter what you do to it, because it can't execute the newer Intel instructions used.

I think you are in a situation comparable to upgrading a component stereo system. You want to buy stuff that is better than what you have, but not so new that it obsoletes everything you own.

Consider moving up to a Mac with ThunderBolt-3, and you can add a ThunderBolt expansion chassis. These were originally marketed for an external graphics card, but some have multiple slots that could accept you PCIe card.