Psijic Order questline is completely separate from the Summerset main questline and the Daedric War storyline, though unlocking it requires the first quest to be done.

If you want to do things in order, you can just leave the Summerset questline for now and complete Morrowind + Clockwork City, then continue the Summerset questline. If you want the "full" experience, the Dark Brotherhood DLC has a side quest called the "Sweetroll Killer", which is relevant to a side quest chain in Morrowind, which is then in turn connected to Summerset. I believe there's also a Prologue quest for Morrowind (and I think CWC as well?), but I cannot for the life of me remember at this moment what it was called and whether you can accept it from the Crown Store interface like you can with other prologue quests, though I assume that is indeed the case.

If you want the full full experience... Complete the base game Main Questline, then complete the Wrothgar main quest line, after which you'll get to see the original "tease" for the Daedric War storyline, as a familiar face from the base game Main Quest gives you an ominous warning.