Same, although I am surprised because busses in cities skylines are usually still affected by car traffic issues. Trains would run perfectly though.

So because the number of active vehicles is much lower than reality, the road network is actually a lot more efficient: it’s a nearly 1:1 scale city with less than a fifth of the real vehicles that would take up the streets. Mostly because of this, public transport in game is a lot better than our particular reality. In fact, the trains are completely underutilized - we can tweak transport modal share (and should) to get the numbers to balance better.

I suspect it's missing the traffic coming into the city from outside

No, that’s modeled in. Those lanes are always active.