I believe it's all virtualized today
I did a tour of Adelaide airport with Engineers Australia in the 1990s. We visited their obsolete IBM main frame, still running ATC in their computer room. They were tied to it by the certification of the software it was running. Just as you described.
There are contingencies for radio outages, but yeah, everything going down at once (if that's what's happening here, which I doubt) is bad.
I would hope that airports keep a battery operated radio + antenna in case of emergency with them, to at least communicate with aircraft within visual range of the airport.
So it falls back to local control, more in the style of visual flight rules. Pilots in existing flights will have to be vigilant and do their own deconflictation and stop new flights out until the network is back up.
All conjecture at this stage of course, but all the radios won't just fail. It is probably going to be a poster child example about the dangers of large scale integration. The attraction of course is that integration is very efficient, the danger is it tend to fail all at once instead of in smaller pieces.
https://www.nbcdfw.com/news/tech/a-calamity-disrupting-hundr...
"we stuck digital computers into a purely analog pipeline, now with software containing a near-infinite amount of lines of code generated by LLMs, to make sure it's capable of a wide range of harrowing, incomprehensible failures."
And everybody here on HN applauds.
Attention: National Radar Outage