Hi Brian,
Thank you for posting and sharing such information with us in forum community. We will try our best to provide you possible information from
our end in the forum community.
Based on your mentioned description, at once we would like to share such information with you as a reference purpose. Generally, Teams status changes to Away when user lock their computer or when it enters idle
or sleep mode. On mobile, user’s presence status changes to Away whenever the Teams app is in the background. Here is the official detailed information article for the reference purpose:
User presence in Teams
Further, at once we would like to suggest you that if you are using Teams application on multiple way such as Teams desktop client, Teams web app client and mobile devices, please open Teams on web browser and
try to identify such result from Teams web app client about Teams presence (Please temporary disconnect Teams application from multiple device, Teams desktop client and Teams mobile device).
On the other hand, if your status has changed to Away, please try to manually change status from Away to Online and see the result outcome on Teams, after running some other application outside Teams.
Here is the information article for the reference:
Change your status in Teams
Here is the screenshot for an example purpose:

Meanwhile, if you are using Windows 10 operating system, please try to perform
clean boot operating system and see the result outcome.
Please feel free to contact us with some updated information so we can further provide you information accordingly.
Regards,
Darpan