Unfortunately, I don't have a save where I haven't done Syri's quest & Puppyslutmass. You can probably speedrun it with this save (Charge Weapon boosts Drone damage). As suspected, Syri invites on Uveto, but not as Crew, unless there's something I'm missing.
I'd like to bring this up before Christmas, because I don't think it was fixed. Unfortunately, non-recruited Anno & Syri aren't issuing the invitation in a new game with Christmas enabled, so I'm guessing it's gated behind real-time, but I don't feel comfortable messing with my system clock to make sure.
I haven't checked the save files recently, but the conditions are as follows (yes, enabling the holiday cheat should also work):
Prerequisites for both: Kaede is able to roam (not on vacation on Canadia Station), is Christmas season, hasn't done the Puppyslutmas before
Anno: Anno is Crew (onboard ship), Anno hasn't offered before, and Kaede has been met (this may be a mistake since Kaede can be introduced for the first time at the party). Invite procs while inside ship.
Syri (Mhen'ga): Has sexed her at least once, Syri hasn't offered before, and Kaede is roaming (though not needing to be met beforehand). Invite procs when approaching her in the morning (before 12:00).
Syri (Uveto): Has done Syri's Quest (either refused or completed) or Syri is Crewmember (not necessarily onboard ship), Syri at The Freezer on Uveto, Syri hasn't offered before, Syri is Friends with benefits (talked to her about various topics). Invite procs when approaching her in the morning (before 12:00).