I've got a theory...
Autodiscover.xml, the autodiscover endpoint that clients use.

Going through the auto discover documentation I came across <ExternalPhotosUrl>
https://docs.microsoft.com/en-us/openspecs/exchange_server_protocols/ms-oxwsphoto/b83a4bba-9ac2-4d1c-aa1a-49c51e614bde

Could potentially play with this using our ability to override the autodiscover XML. This might be something we want to investigate because that'd be pretty neato showing the user's icon from SM in their clients. I'll keep my eye on the thread and I might bring this up with the team as a potential.

EDIT: Here was a blog post I came across while digging around, I didn't read it all the way through but it looks like it touches this subject too,
https://ingogegenwarth.wordpress.com/2018/07/06/sfb-broken-profile-pics/

EDIT2: Depending on my day tomorrow I'll probably test this and see what it can do.

Thanks Matt, interested to see what you come up with! As having a bunch of icons, then just some letters on the sidebar def looks out of place, would be cool if SM could render an icon from the domain's settings and even be overridable by the user.

Edit: I figured you guys would also have a better line of communication with Microsoft to see how this works than we would too.

I think this is in fact Verified Mark Certificates (VMCs) + Brand Indicators for Message Identification (BIMI). We do plan to roll this out sometime in the future and was wondering if SmarterMail supports displaying BIMIs. But even if it does not, setting this up for other compatible clients to display is not necessarily related to SM.

Some resources:
https://www.digicert.com/tls-ssl/verified-mark-certificates

After checking this, the university domain has no BIMI record setup, nor does iCloud or gmail.

https://m365admin.handsontek.net/organization-logos-in-outlook-for-ios-and-android/ it’s something related to azure AD it appears. 

OK, that also makes sense.

About GMail, it is my understanding that they are one of the few that fully support BIMI, however, you actually have to receive email from Google (not through Google) to get a BIMI logo from them.

Anyway, then I guess there are several ways of achieving this, to answer the OP`s original question, but BIMI would work independent of the hosting or mail server one uses (as long as DMARK is also supported, since BIMI is an extension of that as I understand it). But of course, the recipient needs a mail client that also supports BIM. 

What type of account has the icon? I've attempted something but for my account its showing me the Exchange icon for my account no matter what.

Matt,

It's an Exchange account, I believe they use O365.

After looking into this more, it looks like there isn't really anything that can be done in SmarterMail.

The information that Matt found regarding <ExternalPhotosUrl> in the autodiscover documentation appears to be unused. Testing against both Exchange 2019 and Outlook.com accounts indicates that <ExternalPhotosUrl> is not being used. Attempts to use the recommended URL specified in the documentation about <ExternalPhotosUrl> result in 404 - Not Found response from both Exchange and Outlook.com.

We also did some extensive testing with the Outlook Mobile app, and it appears that it has some unusual built-in behavior. When testing, we discovered that Outlook Mobile only shows a user profile pic if it is connected to only one account, and that account is on Outlook.com. After adding another account from any email provider, Outlook Mobile began displaying the Outlook.com account with the Outlook icon. Further, when connecting to an account using EAS, Outlook Mobile appears to automatically assume the account is on an Exchange server, and displays it with the Exchange server icon. If Outlook Mobile is connected to multiple accounts from the same hosting provider, or from an unrecognized provider, Outlook Mobile displayed each account with a colored circle containing the first letter of the email address.

With that in mind, it seems that custom images - such as the college logo in the example from echoDreamz - are handled through some unknown mechanism. Given the way that Outlook Mobile functions, we don't really have a way to identify how it is determining that it should use that specific icon.

Yeah, thanks for the help and looking that over.

I think it is based on Organization logos in Outlook for iOS and Android - M365 Admin (handsontek.net)  something with Azure AD.