Improve documentation search from python.org

Use case

A new user makes a good point that searching python.org is unhelpful: https://www.python.org/search/?q=json.dumps . The search returns "No results found." The current Django python.org search only searches the site's content itself.

Goal

Improve the user experience.

Considerations

The python.org site is a PSF asset and changes to the site would need to be supported by PSF and their infra team.

Possible solutions from least effort to most effort

• Do nothing. Keep the status quo.
• Make the PSF aware of this behavior and ask what they would like to do
• Work with PSF to implement an addition to the search results page on python.org: "If you don't find what you need here, try searching at https://docs.python.org/"
• Add an explicit documentation search button that redirects to docs.python.org's search.
• Develop integrated search on python.org site. This would be a PSF effort.

Summary

For now this is a bit out of scope for the docs-community to tackle alone. Any change would be a joint PSF and CPython docs effort with the PSF taking the lead. cc/ @python/editorial-board

Start by reproducing the current Django search behavior at python.org/search/?q=json.dumps and compare it with the search experience on docs.python.org. Review the proposed options with the PSF and its infrastructure team; done requires an agreed, PSF-supported scope rather than an independent docs-community change.