I have tried to set a message not allowing the user to close it.
In a form add an element of the message type
Add the text you need.
Do not check on "Allow users to close the message"
Save.
After doing that, at least in my case, the message is closable anyway.
In the YAML code appears: '#message_close': true when activated, and it does not appear when not activated, so I also tried adding the code '#message_close': false but there were no improvements...
Closed: works as designed
6.2
Code
What admin theme are you using?
The Gin Admin Theme always included the X/close link.
Via Claro, the close button is not displayed.