What alternative wireless communication form exists that might survive such disruption i.e. is less prone to interference than radio waves.
Free-space optical communication. Lasers and LEDs and photodiodes and so on. It can only be line of sight, and long range links are generally point-to-point, but it does exist and work right now. You couldn't keep your mobile phone in your pocket any more, but other than that these things could be replaced with new technologies and carry on working. Quite a lot of these devices are already in use and in production, though getting enough out to relink the radio-networked bits of world will probably take some time.
Remember that communication with sattelites is only line-of-sight... launching a new optical-only satellite constellation would be a major undertaking, but it is just money and time. The technology is already available.
Is there any science or science-adjacent justification for why some kinds of radio signals still work while others don't?
Shortwave bounces off the ionosphere. Microwaves can be scattered off the troposphere. VHF and the like is line of sight, mostly, but you can still do stuff like bounce it off the moon.
These are all very, very difference mechanisms because the behaviour of radio changes drastically at different frequency ranges. One mechanism won't break them all, unless it is basically magic. A deliberately engineered attempt to break all of them could be done with force majeure.
There are many techniques like frequency hopping spread spectrum, and clever communication protocols like WSPR which are highly resilient to noise and jamming.
Alternatively, can providing more power to a radio transmission overcome such interference or not
Depends entirely on the nature of the interference. Handwave it as you wish.
Finally, is there a possibility that wired communication might also be disrupted?
Doubtful, at best. Something like a Carrington event might affect some radio and some wired communications, and of course you're discussing something that may as well be magic, so you can feel free to define its scope. Fibre optic certainly not.