Changes since congestion pricing started in New York

I wonder if this will eventually lead to increased density and if that then leads to congested bike lanes. Will the cities of tomorrow regulate traffic between individual buildings?

Make no mistake, bikes are much, much, better for urban centers than cars. But the overall problem isn't cars, it's individual traffic in densely populated areas.

Certain policy here in Europe simply assumes that people stay in their surroundings ("15 minute city") and rarely, if ever, visit parts that are farther away individually.

Public transportation, however, is naturally biased. It can be much quicker to get 10km north-south than 5km east-west, or the other way around, depending on the city. And, of course, public transportation is often lacking quality compared to individual traffic. (Taking a bike across a bicycle road vs. getting into a crammed subway train in July, for instance.)

There are a couple of places in the Netherlands with congested bike lanes, which is a great problem to have. It's crazy to imagine all those people in individual cars; we'd have reached congestion so much sooner. (Note that this is after decades of continuously improving bicycle infrastructure; basically everywhere else won't run into this problem any time soon.)

The problem isn't so much density (I think NYC is much denser), as much as it is the existence of really popular destinations; you'll see this close to some big train stations in rush hour, for example. Solutions are smarter road layout, and providing more and more attractive alternative routes, and alternative destinations (e.g. more train stations nearby).