Posting the Answer for better knowledge
Copying from @Rama-MSFT comments
available only within specific teams,
Yes, we can make the application with in specific teams.
not available on group or personal chats,
Yes, we can enable teams, but not for personal chats.
regular users should not be able to install App anywhere,
If you don't want to make the app as public, for specific people we can provide an alternative solution.
admins and team owners can add App to the team
Yes, we can adjust the admins and team owners in settings.