In retrospect this doesn't make sense, to me

When Alicent goes to dragonstone to betray everyone and give Rhaenyra intel (a terrible choice by Condal in my opinion, but topic for another day), why didn't she mention the triarchy?

She told Rhaenyra about Aegon being bed ridden, Aemond planning to go meet Criston at Harrenhal, Ormund's army advancing, but not the triarchy. Alicent was in the room when Aemond said he'd send for the triarchy to break the blockade, so she knew.

Or was it that the writers still wanted it to be a surprise for the blacks when the triarchy arrives?

If Alicent is really just throwing up the white flag, why not mention the triarchy? They're not even letting Alicent be good at treason.