I guess the mail client just talks with MS, submits the data and actually the “MUA” sits in the MS cloud and does all the rest. It is not like with a browser where you see an URL you connect to and can check the cert. You enter your mail server and your credentials and then you have a representation of your mailbox with your mails. (2/4)
Actually a browser could do that, too since they represent that you are entering a URL and get a page displayed. But a “browser” could also be transmitting just the URL to some cloud machine which will do everything for you and then the “browser” on your machine displays the page and everything. Bit nobody did it so far. (3/4)