The city builder genre seems to be few and far between, best I can tell. Cities Skylines comes to mind as one of the more recent examples, but given that its cars have a habit of appearing from and vanishing into thin air, I'd guess its traffic simulation is rudimentary at best.
You might have better luck with titles like transport tycoon or their FOSS counterparts, but those tend to lean into the economic aspect, so I'd expect their traffic simulation to take a backseat, as well.

Don't know about Cities Skylines 2 but the first one is pretty good with its simulation. Adding ways for pedestrians and public transport have a measurable impact on traffic.

That traffic simulation also makes it pretty hard. Most big cities die due to traffic if you don't manage it well.

Mods and DLCs also greatly increase the possibilities and tools available to you.

I'm not sure if anything has really surpassed SimCity 4 yet, especially with mods like:

https://community.simtropolis.com/files/file/26793-network-addon-mod-nam-cross-platform/

That still won't get you the simulation fidelity you're looking for though. City simulators have been dead in the water for a long time.

This thread is a little older but I wanted to second Workers & Resources. It's like a mash up of a transport tycoon and a city builder. Fantastic game, I've put over 700 hours into it and I still feel like a noob.

Maybe Workers and Resources if you set traffic to complex? It's supposed to be a very micromanagey game.

!citybuilders@sh.itjust.works might be able to help you too.

Really would love a good city sim with bikes!