Latest OS for Mac Pro (Late 2013)?

Current Adobe Photoshop update alert calls for OS 13.4.0. I believe this OS is not compatible with Mac Pro (Late 2013). I am already have odd redraw issues using Photoshop (my primary work app).

Currently using OS 12.6.7 for which I see there is an update to OS 12.6.9

What is the latest OS that I can safely run on this computer?

I have had issues in the past with hardware becoming incompatible with OS Updates. I'm also not convinced that the current Mac hardware options aren't at the end of their series cycle.