Unable to log in to iMessage and FaceTime on my Mac mini running Sequoia

Dear all, please help!

I have difficulties to login to my IMessage and Face Time on my Mac mini M2 Pro (Sequoia).

I tried everything, read and watched all video tutorials how to set iphone, ipad and mac to work with IMessages, and without any success.

Yes, a am logged to identical Aplle ID on every device, I have all settings set on my Iphone and Ipad (btw, between those two, everything works wonderfully), but I can’t get to Mac IMessages setting because everything is grayed out.   

So, at this moment I am stuck on login screen with endless rotating circle (after entering my Apple ID user and password). Also, my Iphone mirroring doesn’t work.

I tried identical settings with my other (work) Apple ID and everything works perfectly!

Is there way to reset all settings on my “problematic” Apple ID, or to reset IMessages and FaceTime app on mac from Terminal to start from the beginning?

Is there way out from this mystery? :)

Thank you all in advance!

Best regards!

Alexander

[Re-Titled by Moderator]