How well could meshtastic work in a natural or man made disaster where internet and power grids are down?

If its solar powered, then it should work to some capacity.

One of Meshtastic's common applications is standalone solar nodes that just sit on the top of a large hill or mountain and relay messages "indefinitely". There are a few in my area and it enables basic text communication even if there was no internet or power grid. Here's a recent video on building a solar Meshtastic node: https://www.youtube.com/watch?v=oCrBMthrCKc

There are limitations. It scales well with a maximum number of around 70-80 nodes, which is a quite low number.

IIRC that's per-channel, but nodes can relay data for channels they aren't members of

I recently learned you can attach garden light solar panels to audio jacks to turn vibrations in light into sound.

I mounted two in a suitcase to make a DIY synth.

https://www.instagram.com/reel/C2L2k3ZNBTC/

It's such an easy and fun hack.

How does the sound change if you use a candle or some other analog light source? (or even a DC battery with a non-LED light?)

If it is a solid light there is no sound. It is the change in light value that makes the sound. A candle flame would make a wobbly electric signal that you could use as a control on a CV modular synth but it wouldn't be much of an audible sound on its own.