After what seemed like a very long period of time just scrambling over rooftops looking for chests and collectables, I finally decided to pursue the main questline again. Well, after a mission or two for the theatre, anyway.
The next mission was the one where you have to infiltrate Notre Dame and assassinate Sivert. Of course, I messed it up a few times mainly by being spotted or not planning my escape. Eventually, I got my act together and did it properly, or at least an approximation of properly, by taking down Sivert’s associate first, nabbing his keys, and then waiting in the confessional ready to do this:
After that, there was some bizarreness involving portals and timeshifting and jumping between servers or something. Frankly, it didn’t make a lot of sense, and required me to avoid trains, climb the Statue of Liberty, not be hit by flying debris and outrun and avoid data corruption. Or something.
Finally, I returned to wandering around doing good deeds, collecting those rosette things, and generally running into people and knocking them over. As you do.