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I can't believe it's been over 2 years and the issue still exist. Recently I found out that the time for the status switches "Available" to "Away" has been shortened. This is the most annoying feature that Team has.
The engineering team is continuing to work on adding support for multiple accounts on desktop clients. We will first launch support for 1 work/school account and 1 personal account so users can enjoy Teams for work and personal side-by-side. Windows and MacOS. Support for multiple work accounts is still being worked on and will come at a later date.
You can track status via the roadmap here: https://www.microsoft.com/microsoft-365/roadmap?searchterms=68845.