This episode was a lot, and only the last step toward a conclusion of the season arc(s). I'm going to try and post as I form thoughts about specific themes...

"The church on Ruby Road"

There are definitely elements carried over from this one into the entire show since then. First, the themes of coincidence and luck, and perhaps by extension wishes (and doubt?). It seems like RTD is still grappling with telling them apart, like with the unfortunate Zufall family who nominally belonged in one category, but were played according to one or several others.

There was nothing Zufällig about the Rani finding the seventh son of a seventh son of a seventh son. That's a traceable anomaly, a standout pattern that portends the specialness of the child. More than an omen, an identical lineage might be engineered to similar effects — in which case we are uncomfortably close to the magical thinking of eugenics.

Our showrunner would make a poor practical magician if he can't separate happenstance from wishes that have more intent behind them, a "gamification" perhaps of randomness, or the methodical identification of patterns in (apparent) coincidence. However, he did also introduce the "technology of rope" in "TcoRR". That's a fairly scientific approach that requires a deeper understanding of a field's taxonomies and the patterns inherent in them.

We might expect that stringency of method from the Rani, and so far it has been suggested as much in behind the scenes interviews. We will have to wait and see if her scientific applications of coincidence shows on screen. I think only then do we have a proper synthesis of science fantasy in the show.

So those are two components from the first christmas special that have set the course for the following seasons. Superstition, and its scuentific formalisation. The third, most glaring one is — all the babies. I don't think we've ever had so many orphans, foundlings, kidnappings, and (space) baby factories in the span of two seasons before... and then there is the baby elephant in the room, the Timeless Child.

Right now, Doctor Who has more unknown parents in play than in your average soap opera. I'm not even going to speculate which are going to be tied up, or how. At best, it's going to be a pattern we won't recognise until it's shown to us.

Catching up on Omega is as easy as Rani homework was. His broadcast appearances are pretty scarce.

It's "The three Doctors" and "Arc of infinity" — and again the second one really does feel like homework — plus "Remembrance of the Daleks" for additional credit, even though it's only the Hand of Omega that appears there.

But you sort of owe yourself any chance to watch Sylvester McCoy dropping clues to the Cartmel plan, so do take "Remembrance" if you can!