auto-update index for myst website

[dellaert]

When I preview a myst-generated website using myst start and I add index terms, the index does not auto-update the index page on the preview website. I have to kill and restart the preview. That could be by design, but it would be very cool if the index auto-updated :-)

Proposal

auto-update the index page whenever an index item was added, modified, or deleted.

Additional notes

• The new index feature is amazing, thanks @fwkoch and @rowanc1 !
• I am running myst start inside the robotics book repo.