“Activating a venv” just manipulates some environment variables so that the prompt changes, PATH changes and a deactivate command exists. Installing to the venv can be done just as easily by running the venv’s Pip using the venv’s Python, which in turn can be done by explicitly specifying the path to that Python and using -m pip instead of running Pip directly. That’s how I’ve done it in the example.
I think you’ve missed the point of the thread. The cache directory apparently contains wheels (or at least, binary blobs that include wheels) in other sub-folders, and Pip knows how to use those wheels for installation; but pip cache list only shows what’s stored in the wheels subdirectory (i.e., wheels that were built locally, not downloaded).