SPFx 1.10 was released recently which now includes support for Teams personal apps. Catch the announcement here: https://developer.microsoft.com/en-us/sharepoint/blogs/announcing-sharepoint-framework-1-10-extending-sharepoint-framework-across-microsoft-365/
To deploy a personal app with an SPFx package, you have the option of deploying the package to the SharePoint tenant app catalog and clicking on the "Sync to Teams" button which then makes the app available in Teams as shown here: https://docs.microsoft.com/en-us/sharepoint/dev/spfx/integrate-with-teams-introduction
But what if you are coming at it from the Teams app point of view? You already have a Teams app with a bot or a messaging extension and want to add the SPFx powered personal app to it. You probably don't want to use the "Sync to Teams" option in this case because then your SPFx web-part will be available as a separate app in the Teams app catalog.
Fortunately, it's very simple to define a staticTab in the Teams manifest which points to the SPFx webpart. This then makes the SPFx webpart available as a teams personal app:
Notice the teams and personal query string parameters as they are very important. You will also have to replace the component id with the id of your web-part.
I have also updated the official MS Docs with this approach:
Thanks to my colleague Jarbas for working with me in figuring out this one!