Thank you @leroydouglas for your quick reply.
These two links didn't help unfortunately:
Use an iPad as a second display for a Mac - Apple Support
Universal Control: Use a single keyboard and mouse between Mac and iPad - Apple Support
But changing the AirDrop option from "All" to "Contacts Only" changed the error message when I want to connect to the iPad now:
"A miscellaneous error occurred (-6745)"

I found out there is another thread about the specific error message already:
A miscellaneous error occurred (-6745) - Apple Community
The only solution that was provided in that thread was to uninstall Norton Security. I don't use Norton but I have Eset Endpoint Security installed. However I can't uninstall it because it's mandatory for me due to the company policy.
So I checked what the error code "-6745" means. Here's the answer provided by chatGPT:
Error code -6745 on macOS is not commonly documented in public resources, making it challenging to determine its exact cause without additional context. This code may be associated with specific applications or system processes. To address this issue, consider the following steps:
1. Identify Recent Changes: Reflect on any recent installations, updates, or system changes that preceded the appearance of this error. This can help pinpoint the source of the problem.
2. Consult Console Logs: Use the Console app (located in Applications > Utilities) to review system logs for any entries related to the error code. This may provide insights into the underlying issue.
3. Update Software: Ensure that all your applications and macOS are up to date, as software updates often include fixes for known issues.
4. Contact Support: If the error persists, consider reaching out to Apple Support or the support team of the specific application involved for further assistance.
Answer to 1:
No recent changes.
Answer to 2:
I don't know how to interpret the system log :( Is there anybody who has experience with the error code?
Answer to 3:
All applications are up to date.
Answer to 4:
Contacting support would be my last option.