UPDATE: Support for VS 2022 was added recently in TDS.
You have to use the x64
.msi file which is included in the most recent TDS version 126.96.36.199 released on November 12th, 2021 while VS 2019 only works with the x86
.msi (also included).
As of now it is not possible to use TDS extension and many more VS extensions in Visual Studio 2022.
Reason is because VS 2022 is 64-bit and so far all VS extensions in marketplace were being built as 32-bit for VS 2019 and earlier versions.
All third parties extensions (like ReSharper) will be updated for new 64-bit version as we approach general availability of VS 2022 then it should be possible.