Uber?

Nope, no Uber in Germany. You may see signs advertising it, but it is not the same and I think they did a lot of marketing before their business model was ruled illegal by the German government.
Even small towns have buses or taxis and along the Rhine there are trains. Both sides, going both directions.

I've used the Free Now app (formerly MyTaxi) to get cabs in Germany. Works a lot like Uber... except a cab comes instead of an independent contractor.

https://free-now.com/

The company covers 45 cities in Germany (per their website), including: Aachen, Berlin, Bochum, Bonn, Bremen, Köln, Dortmund, Dresden, Düsseldorf, Duisburg, Essen, Erlangen, Frankfurt, Hamburg, Hannover, Ingolstadt, Leipzig, Lübeck, Mannheim, München, Mülheim a.d.R., Nürnberg, Offenbach, Potsdam, Stuttgart, Wiesbaden

I completely believe you, Ms Jo, when you say that Uber does not operate in Germany. And I know that my cousins, who live in Frankfurt, called for me (Oct 2019, the day I saw you, Ms Jo!) what they referred to as an Uber. They called it on an app. And the vehicle that showed up was a person with an unmarked car, rather than a marked taxi. I don't recall whether he had an Uber sign in the vehicle. I do recall that we checked the license plate against the app.

Perhaps they are referring to it as Uber, but it is something else and they're just used to using the Uber name? In any case, to me as a user, it seemed to serve the same function as Uber, as we think of it in the US.

Uber apparently is active in some form in a few German cities: https://www.uber.com/global/en/cities/

Berlin
Cologne
Dusseldorf
Frankfurt
Hamburg
Munich
Stuttgart

I remember seeing Uber ads at Tegel when I was there in the fall.

As an aside, I learned Free Now is backed by Daimler and BMW

Uber's basic business model is illegal in Germany because private persons are not allowed to offer commericial co-rides.

Uber X (calling you a limousine service) is operating in some cities but not real cheaper than taxis which are allowed to use bus lanes; Uber is not allowed to do so and stands with other cars in the traffic jam.

In Berlin best co-rides are offered by BerlKoenig and by CleverShuttle. Public transport is often faster and definitely cheaper.

What I dislike most is that Uber drivers operate often not confirm to law because limo services are not permitted to wait in town for next order, they have to return to base. In Berlin most Uber drivers do not do so in Berlin and Uber is fully aware of this without stopping this illegal behavour.

When you are doing business in Germany I woud NEVER show up with Uber sending the signal that you support illegal behaviors. Some Germans really do not like that - including me.

Just use the electric scooters (I used Lime), great fun to get around.