Ok small update. I flew away from the planet and then back again and re-entered the base. I managed to move the mission on by flicking some switches to access the core room... but... now it tells me to destroy the core, but I already have.

I tried placing another core and then destroyed it instead but it still didn't work.

At a loss on how to proceed now.

There is a command to reset a poi, but I can't recall what it is, I do remember that you'll need to find the poi ID. Sorry can't remember the command for that either and a quick Google search didn't help.

https://empyrion.fandom.com/wiki/Console_commands_regenerate

Found this, I believe it's the command I used previously.

Hope it helps.

Thank you TheHellKat, this worked and I was able to redo the whole mission (which was a pain) and finally complete the mission! I appreciate your help and support.

No worries, glad to be able to help.
I had a similar issue with the comm base, the pda didn't update after blowing the core, took me a little while to find this fix.

You could have also went to another planet with a rados drone base and killed that.