I‘m a little shocked rn. I am using fluffychat on ios since my legacy iphone is still working and I dont want to throw it out until its done.
But this happened the first time: I wrote „then I might need to take a taxi“ to someone and an installed taxi app immediately popped up via notifications saying „get off 25% today“ or something.
This freaks me out big time since it could mean every word I write on this phone gets checked by something/someone.
Anyone else? (It was literally the second I wrote the sentence)
No. If someone is telling you that Apple is doing that, they are lying to you. Demand proof, because no one can provide that. Because Apple is not doing that, and if they’re telling you they are, they are lying.
If you demand proof to state they do, you should provide proof when stating they don’t. It’s not like Apple is the most trustworthy company in the world. With big tech it’s always reasonable (definitely not certain) to assume they could be spying on your activity, and unless you are able to download your software source code, check it and compile it yourself, it’s almost impossible to tell.
Until it’s proven the data is E2E encrypted, it’s a fair assumption it can be read by a 3rd party, either now or in the future. E2EE is the only proof that matters, everything else is just a corporate “trust me bro”.
Prove it
While I get the initial claim that proof is necessary, your argument is self-evident as well.
Nobody can provide proof does not mean its not true, just that its not proven. Its very suspicious that I got this notification the exact second I wrote the text and no other notifications for days before and after.
It is statistically very likely that someone or something triggered this in that moment. Either on the phone through siri for example who is supposed to select apps by usage, in the chat app (unlikely because open source) or in the notification provider, as mentioned by another commenter.
So you admit that you can’t back up your claims. Don’t expect reasonable or rational people to believe you. 
Are you joking? When did I claim anything? I said this happened, not that I know why.