Host Computer SMT P Outgoing Server

I mean, an outgoing mail server is not exactly a property of a computer, it is set in the mail client and one can have any number of them. It is not something fix assigned to a particular computer like MAC address or so. It depends entirely on the user what server he is using. Every user can have any number of smtp servers in use.
And webmails have there own servers, each of them different one and you can get them from the website of the webmail provider. Such information you can not find on the particular workstation (in simple way), the information is on the webmail sever.

And this is also the case, when the internet cafe operator has its own mailserver set up. In such case the mailserver is just contacted via the webmail interface and giving essential data to it and the mailserver itself will take care of those data.

The question what mailserver is connected to the particular workstation is similar as if you ask what webserver is connected to that computer. The answer would many many millions, namely all webservers on internet. So all mail servers on internet are also connected to the computer in front of you.

On the other hand, I could imagine someone could create some kind of program which could search for setting in known mail clients, like outlook, Thunderbird, or what ever and display those, but I am just wondering what practical use might be behind it.