You can construct the .vsix download URL by hand.

1. Get extension's "Unique Identifier", and split it into two parts along the .:

   eg. ms-python.python becomes ms-python and python

2. Get a version from "Version History" tab on marketplace.

   eg. 2024.17.2024100401

3. Determine the binary type that you need. Skip this step if this extension is "Universal". Note that some extensions do not support all binary types.

   Binary type	targetPlatform
   Alpine Linux 64 bit	alpine-x64
   Alpine Linux ARM64	alpine-arm64
   Linux ARM32	linux-armhf
   Linux ARM64	linux-arm64
   Linux x64	linux-x64
   Windows ARM	win32-arm64
   Windows x64	win32-x64
   macOS Apple Silicon	darwin-arm64
   macOS Intel	darwin-x64

4. Combine

   https://marketplace.visualstudio.com/_apis/public/gallery/publishers/ms-python/vsextensions/python/2024.17.2024100401/vspackage?targetPlatform=win32-x64

   The ?targetPlatform=win32-x64 part is optional, if your extension is universal.

In Python:

unique_identifier = 'ms-python.python'
version = '2024.17.2024100401'
target_platform = 'win32-x64'

publisher, package = unique_identifier.split('.')
url = (
    f'https://marketplace.visualstudio.com/_apis/public/gallery/publishers/{publisher}/vsextensions/{package}/{version}/vspackage'
    + (f'?targetPlatform={target_platform}' if target_platform else ''))
print(url)

The debug bits of the Microsoft Python extension have been extracted to the Microsoft Python DebugPy extension. You can find the announcement here. Make sure the ms-python.debugpy extension is installed (it should be installed automatically as part of the Python extension update), and that it's enabled. If I remember correctly, it was disabled for me by default for some reason.

You might need to create a launch config to use F5 to launch. See also https://stackoverflow.com/a/77937940/11107541.