FYI, all I needed is to run Zed with Administrator privileges so that Zed’s extension installation process can place the extension’s final artifacts (e.g., the compiled extension.wasm) into specific directories.
Thank you o1...

Fixed that Cargo, here is the related logs. 4 hours on it later, still no extension visible.
One suspicious error:
A required privilege is not held by the client. (os error 1314)

At this point I'm ready to pay you to fix my Cargo...

Of course I've followed the docs, my issue isn't with developing but with installing it which did create a .wasm file and /target/wasm32-wasip1 folder. Yet can't find it in list.

Only extension-related log is:
[INFO] extensions updated. loading 1, reloading 0, unloading 0
(only loading html ext)