Dear Kristopher E. Steinebach,
Good day! Thank you for posting to Microsoft Community. We are happy to help you.
We have location and job title information for our Microsoft 365 users, however Teams is unable to load search results based on that information.
Please refer to this document for this inquiry: User information isn't updated in Microsoft Teams - Microsoft Teams | Microsoft Learn
After finding the correct person, I would then like to be able to push a link to initiate a Teams call.
So far, based on my tests, the SharePoint for iOS app really doesn't have such built-in features to meet your needs, I completely agree with you, this is indeed a good addition to the current features of SharePoint for iOS, thank you for pointing this out. Microsoft continuously aim to improve the features of O365 Product and suggestions like this is very much appreciated. You can go to Feedback community to create a new entry or vote this entry.
Sincerely,
Tin | Microsoft Community Moderator