I’m afraid that it doesn’t support this feature on Teams for Linux client.
In windows client, you can select the option “Open application in background” to allow Microsoft teams to launch to the system tray. However, in Linux client, it is no such option. The following picture do a comparison:
we recommend you that please give a feedback to https://microsoftteams.uservoice.com/forums/555103-public/suggestions/39970093-how-to-start-ms-teams-minimized-to-tray-ubutnu-18 . Microsoft will always focus on customer’s feedback and experience. some new features would be added to the services based on customers' feedback in the future, and your good ideas will be very helpful for them to improve the service.
Your time, understanding and cooperation will be highly appreciated.