in EU it's normal

- a company run the busses

- its partially of fully owned by the city/state, i.e. NOT private investors, not private liquidity, no one expects any payouts

- its commonly a special form of "company", e.g. "Anstalt des öffentlichen Rechts" in this case which you can roughly read as "installment/company based on public-law"

Practical that is "mostly" the same as state run when looking at it from a distance. But with some differences. Like it's still a company, has it's own company structure, it's own bookkeeping, it's own employees etc. This leads to a much more clean separation when it comes to budged managing, and where possible removes/reduces direct political influence into daily operations (just direct one, indirectly through ownership etc. there is very much still influence, but this makes it somewhat less suspect to damage from changing political parties non stop changing directions).

Through things can get far more complicated then just one company, in one legal form.

It's usually a company owned by the city or the state, e.g. https://en.wikipedia.org/wiki/Berliner_Verkehrsbetriebe

Normally municipalities own companies that do the public transport service in Germany

They're usually private companies owned by the cities.