DVI should not control the monitor's actual physical controls - it does include a small non-display channel but IIRC that's used to get the display modes info from the monitor, and potentially to transmit contrast information and the like; some monitors will prevent you from adjusting contrast if DVI sends that info for example, but it certainly shouldn't disable the power button.

My guess would be a hardware issue - in the monitor itself - which is somehow triggered by the sequence in which you do enable the displays, and your system update being unrelated. It's a huge guess though. One thing to try is repeating both sequences (the one that locks your buttons and the one that doesn't) using a live CD - not a "nobara 38" one if such a thing exists, another distro. Trying both monitors on another computer would be an interesting test as well, although not necessarily that helpful (because if it doesn't occur there, it might just mean the issue is triggered by peculiarities in your graphic card).

Unlikely, but who knows? Can you try and boot Windows (install iso probably enough)? Or some very old Linux distro? It might just be your monitor becoming weird with age.

Edit: Alsobtry with a laptop or something and see how it goes.

How old is the Asus monitor? This might also be a hardware problem, bad caps related. Digital equipment is sensitive to power voltage fluctuations, and when bad caps are in the picture, even more so, making the equpment do all sorts of inexplainable things, like how could one thing I do on this monitor reflect on what the other monitor does or doesn't. In most cases, a small ground loop or a fluctuation caused by one of the monitors draining power when being turned on or off, might affect what the other one does or doesn't, if it alredy has failing caps. I've seen similar things happen on dual monitor setups when one of them has failing caps. One turns on just fine the other one doesn't, but you power them in reverse order, hey they work 😂.

My brother had a screen that would occasionally reboot with fullscreen video, but not if you kept some window decoration onscreen. There must've been some degree of (you can not turn it off) image processing that would shit itself. Maybe it was local dimming related.

Everything is filled with software, and a lot of it is hot garbage.