How do I move an old MacMail account (old MacBook late 2009 10.9.5)to another computer MacBook Air 2019 Sonoma 14.6.1?

Have tried many methods so far - migration assistant (computer sees the other one but won't connect)

went to the keychains but can't see the mail app - sorry not the best at all of this.

The old Macmail is still functioning on the old MacBook and works on an iPhone but I can't get it move over to the newer machine - just need to be able to find the password... to the Macmail - all I get is a line of dots and I don't know how to reveal the password at that point. Any help much appreciated - thanks!