I'd love to use a version of this mod / script that gave a server chat message upon first entering a system with respawning asteroids.

Did you make such a version? And if you're still waiting on permission to share, could you please explain what you changed to make it give a chat message instead of displaying the "Shipproblem" icon?

I contacted the devs for some help on this as I was trying to figure out how to stop the icon "pulsing". The function addShipProblem has a final variable "withHighlight" that can be set to false. This will stop the "pulsing" behaviour of the icon.

So, on line 28 of data/scripts/entity/detectrespawningasteroids.lua you can put "false" at the end of the addShipProblem arguments, like so:

addShipProblem("respawning asteroids", Entity().id, "Asteroids respawn in this Sector"%_t, "data/textures/icons/diamond.png", ColorRGB(1.0, 1.0, 1.0), false)

I've done this locally and tested it and it seems to work fine!