I'm a developer on this extension. In the marketplace tab in VSCode you can right click the python extension and select "Install another version" when you do that it will pop up a list of all the old versions of the extension. This should allow you to go back and find the version that works for your VSCode.
Answer from Ian Huff on Stack OverflowFail to install 'ms-python.python'
Unable to install python extension from visual studio code
Unable to install extension 'ms-python.python' as it is not compatible with VS Code '1.77.3'.
MS Python extension won't install with VS Code in user local folder
Close the installation program and follow:
- On the desktop, press Windows key+R to open a Run dialog.
- Type
msiexec /unreg, and press Enter. - Follow the first step again.
- Type
msiexec /regserver, and press Enter.
In this link you can find more information.
- Go to Task Manager -> Details Tab -> End Task 'msiexec.exe'
- Try install again.

I know this is an old post but I recently ran into this exact same issue. It was caused by my machine having pending Windows updates that needed a restart to be applied.
Once you've reset your machine remove the C:\Python27 folder (this is important).
Rerun the installer and it should work with no issues :-)
Please provide the environment you have installed.
if windows 2008 R2, because of the rights issue, you need to cancel the installation of pip, it is best not to install in C.
msiexec.exe /quiet /i python-2.7.10.amd64.msi ADDLOCAL=DefaultFeature TARGETDIR=D:\python27