We did write how a blog on how to check Einstein Analytics License Assignment, this blog will share about checking Inbox license in Salesforce Classic and Lightning.
Inbox License Assignment is pretty similar to Einstein Analytics License Assignment, you can see how many Inbox total licenses you have, how many licenses used and the remaining licenses in Company Information under Permission Sets Licenses in the setup menu.
Next question, I would like to see who has this license assigned? You can run SOQL to get the list of users assigned with Inbox license, here you go
SELECT Name, Id FROM User WHERE Id IN
(SELECT AssigneeId FROM PermissionSetLicenseAssign WHERE PermissionSetLicense.MasterLabel ='Inbox') AND IsActive=true
ORDER BY Name
Next, if I manually open the user detail, how I can see if the license has been assigned? Is it under Permission Set Assignments or Permission Set License Assignments related list? This is exactly the same with the Einstein Analytics licenses assignment, once you add the Permission Set, the Permission Set License will be auto-added, but not the other way round.
From the above screenshot, once you add the "Inbox With Einstein Activity Capture" permission set, the Inbox license will be auto-granted.