Can I connect my smartphone (Android 11) to my laptop (keyboard is permanently installed) in order to write something on my mobile phone on the laptop?
That's fine. I use the app in the mobile phone "MyPhoneExplorer" and the program on the PC.
With it you can enter texts in the mobile phone, make backups and much more. First download the app to your mobile phone, it will tell you how to proceed.
There are app pairs (an app for the smartphone and a corresponding app for the PC / laptop, with which the smartphone screen can be mirrored on the PC monitor. Most of them can also reverse the mouse and keyboard for smartphone control use.
I recently searched for screen mirroring smartphone to PC, but don't remember the URLs Wait a minute, I'll look again.
Search terms: Smartphone PC Screen Keyboard Mouse
Interesting hit: https://www.smartphone-tipp.de/technik/handy-pctastatur/
(but none of those from a few days ago)