Using the Exchange 2010 version of Outlook Web App (OWA) you could click the (?) button and then click About to get a really useful page containing information about the Mailbox server, Proxy server, Client Access server, etc.
Is there an equivalent with the 2016/2019 version of Outlook on the web?
The page is really helpful when doing migrations from Exchange 2010 to a newer version since you can see if the OWA is being proxied as well as where the mailbox resides.