Any good Cities Skylines-style game with support for bike lanes, bus lanes, bike paths and pedestrian paths?

Cities Skylines 2 sounds like it will be better in that respect. They have mixed used buildings and a better road system for adding bus lanes, trams, etc. Won’t be perfect but better than the first game

You can get very close with C:S mods, for example road builder will let you design roads with pretty much any lane configuration you want including bike and pedestrian areas. I'm a very anti-car person and I love C:S because it lets me build a city the way I wish my hometown was. You just have to tweak the game a bit to get away from the car-centric starting progression.

Through many of CS1 DLCs they slowly added more pedestrian/car free infrastructure. City Planner Plays on Youtube has a few detailed videos on the various DLCs and what they add. He also has a few videos on mods to make the CS1 experience more user friendly.

A Netherlands simulator? I'd love to see this.

There is a create on the workshop called Urbanist that has great Street options. There are a couple pedestrian and shared street options

Workers and Resources: Soviet Republic. It doesn't have bike lanes but you can set a fully pedestrianised city, as emergency vehicles can use footpaths if needed. It also has trains, trams, buses and trolleybuses. Also helicopters, which are cool but impractical most of the time. The public transport line management is pretty in depth too, you can have pick up only spots, spots specific for workers or students, drop off only, or a bunch of other parameters. It's really good.

It also has resource management, but the difficulty settings are really granular so you can adjust it to however you like.

Minecraft

The city simulation side is much weaker but there’s Cities in Motion 2. Doesn’t have bike lanes but it provides and interest traffic simulation where you can expand public transit and pedestrian access.

Yes, it's sad, that you always have to build a car city.