Just happened to read about pneumatic tubes around the world in The Victorian Internet. Even though pneumatic tubes were invented after the telegraph, they didn't suffer the same congestion issues as the telegraph (because you could send messages in bulk, I guess?). And unlike how telegram were charged by-the-word, pneumatic tube messages were charged a fixed price. The book focused more on the Paris pneumatic tube network than the Berlin one.
https://en.wikipedia.org/wiki/The_Victorian_Internet
https://parisianfields.com/2018/05/20/les-petits-bleus/