Chrome extension in python?

There is no Python built into Chrome but I am wondering whether pyjs can help you.

You can make AJAX calls to a separate service with Python from your Google Chrome Extension. All complex logic will be moved to separate microservice. There is a video how to create Chrome extension, maybe you will find something there - https://youtu.be/l17LDVytSE8

You can make a standard Google Chrome extension with Python (server-less) https://pythonspot.com/en/create-a-chrome-plugin-with-python/

The idea is to compile Python to Javascript (technically a JS pre-compiler) using Rapydscript. Then include the generated script in the Chrome extension. The site above has a zip file with all the stuff inside.

I recommend using Rapydscript instead of Pyjamas. A Python script compiled with Rapydscript works like any other Chrome plugin.

Pyjamas scripts does not work well with Google Chrome (needs a special parameter when Chrome starts or server).

Although you mentioned you don't want it to be a hosted app, but this is one typical scenario where a hosted app can do.

SciPy is not a package that is easy to deploy. Even if you are writing a installed application based on SciPy, it requires some effort to deploy this dependency. A web application can help here where you put most of the hard-to-deploy dependencies on the server side (which is a one-off thing). And the client side can be really light.