I've gone to the embassy and I've seen the cutscene but everything stops there. Is there something else I'm supposed to do? They mentioned going down in a cave somewhere, but there is no mention of anything in my mission log.

Do I wait until I get tier V?

Underground Ruins

So I need to go to the underground ruins now? I don't have any sort of mission marker for it...

Take the transporter to the underground ruins (it has its own pad) and talk to the Romulan civilian standing there, from whom you get the actual mission. Then go to the entrance to the underground ruins.

Make sure you and your boffs all have EV suits

What's the point of keeping two consoles active anyway? I thought it would fail the mission, when I lost all four consoles, so not sure what the purpose of it all is here. Nothing in the wiki about it, so not sure on that part, despite the mission completing anyway.

You get a bonus reward of some kind (forgot what it was) if you prevent the reactor from overloading.

Actually you don't even need to touch the ruins until T5, and as it's a major pain in the tail, I'd recommend doing exactly that. For the record, saving the plant from overloading netted 5 more marks the one time I managed it around the mass of Tholian spam.

Huh... though it was because some cut scene wouldn't show, or something... if it's just marks, I'll keep my extra EV suits in the bank, and stay the well away from this mission then.

Then ignore just about 30K Dilithium and 750 Romulan Marks that is T5 cutscene viewing.

In short you have to do it as the reward is nothing to sneeze at, however you can just ignore it when hitting T4 and do it when hitting T5 in order to only do it once.