iMessages on MacBook Pro does not respond to my CORRECT Apple ID/password

I am trying to sign in to iMessage with my MacBook Pro (do not know how it got disconnected in the first place).

I put in my Apple ID/Password.

First, it says in 1990s Microsoftian language that an "Unknown error" has occurred.

Then it says upon the second attempt that my Apple ID and password are incorrect.

Upon the third try, as I read the response I hear that snarly sweet Siri voice in my head,

"Have you forgotten your Apple ID/Password??"

No Siri....I have NOT forgotten my Apple ID/Password!

Meanwhile.....I go to my desktop and access the App Store which requires the Apple ID password. It worked just fine, as I knew it would.

I then went to my MacBook Pro and signed out of my Apple ID altogether....iCloud....everything.

Then I went to my iPhone and curiously it said that not all my iCloud features would work until I entered my Apple ID and Password. OK. I did that. No problems. Then it asked me to enter my LogIn password for my MacBook Pro.

"Ahhh," I thought, "now we are getting somewhere!"

I put in my MacBook Pro login password and it was accepted with no problem.

I then went back to my MacBook Pro. I signed into my Apple ID with no problems.

I attempted to sign in to iMessage and......

"An unknown error occurred"

"Your Apple ID/Password is incorrect."

"Have you forgotten your Apple ID/Password?"

Now I just want to scream! It can't be the computer itself, can it???

2016 MacBook Pro (touch bar). 3.3 GHz i7, 16MB RAM running macOS Big Sur 11.5.1

If anyone knows anything at all about this totally bizarre problem, I'd love to hear it (and I'd be grateful too!)

Thank you!