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According to Microsoft 365 roadmap, the Microsoft Teams desktop app may be available in the Microsoft Store as early as May 2022. Of course, this is only an approximate date, which means that the date may well move a few weeks ahead.
Microsoft Teams from the Microsoft Store will support both Windows 10 and Windows 11, though the app itself will vary slightly depending on the operating system you’re using. For example, the Windows 10 version will support personal, work, and school Microsoft accounts, while the Windows 11 version will only work with work and school accounts.
The fact is that in Windows 11 there is a Chat application based on Microsoft Teams, which is intended for personal use, which means that there is no need to install a separate version of Teams from the Microsoft Store. There is no such integration in Windows 10, so the application will support personal accounts.