[Doc] Upgrade example gallery

[peytondmurray]

Why are these changes needed?

This PR updates the example gallery.

• Instead of dynamically removing the default sidebar and repopulating it with filter buttons using a script, here we just create the sidebar at sphinx build time. This has advantages:
  • No script needs to run, better performance
  • No flash of content before the script runs
  • More maintainable: HTML templates hold HTML, rather than JS
• Styles (including icons) have been updated to work with dark/light themes
• tags.js has been renamed to examples.js to more clearly associate it with the example gallery. Code is mostly the same as what we currently have, with just a few selectors changed.

Related issue number

Partially addresses ray-project#37944.
Depends on #2.
PR 4/x targeting ray-project#41115.

Checks

• I've signed off every commit(by using the -s flag, i.e., git commit -s) in this PR.
• I've run scripts/format.sh to lint the changes in this PR.
• I've included any doc changes needed for https://docs.ray.io/en/master/.
  • I've added any new APIs to the API Reference. For example, if I added a
    method in Tune, I've added it in doc/source/tune/api/ under the
    corresponding .rst file.
• I've made sure the tests are passing. Note that there might be a few flaky tests, see the recent failures at https://flakey-tests.ray.io/
• Testing Strategy
  • Unit tests
  • Release tests
  • This PR is not tested :(

[maxpumperla]

Without preview builds, it's impossible to judge how this will come out at the end, but the strategy is brilliant, a clear improvement over what we have.