It has to be the marriage certificate and any provincial picture ID or Driver's License (get your wife to apply for a provincial ID with the marriage name on it as well)
While I agree with the point that photo ID will be required, my reading is that the photo ID does
not have to be updated to reflect new name in order to apply for passport. The point of the photo ID is to confirm identity, not the name, and the photo ID plus other docs
and the legal name change doc (marriage certificate) is enough to establish (new) name.
Now that said: you can run into people in any bureaucracy who won't agree with this, and I strongly doubt the specifics of this point are outlined in their internal regs (even if obvious). And there's no
feasible way to challenge this point in a timely manner (you could go to court and waste time and money). You
might be able to complain to a supervisor, but no way to know in advance how that will go.
So: it definitely is
better if the applicant can eg replace a photo ID with the new name before applying for passport. In Ontario they give you a paper version when you do it, on the spot, and that combined with the photo ID DL card is considered 'new and amended' until you get the new card (and I don't think the passport office people could really argue with that). So I'd recommend that anyone do exactly as you suggested, even if not strictly required, if feasible. (I think the service ontario outlets are mostly past the horrific lines and all that of the pandemic but don't know about other jurisdictions and I'm not certain about that).
But in principle you really shouldn't need to replace everything before you apply for the passport.