We use mkdocs for our company handbook and when running the Wave accessibility evaluation tool we noticed that the search boxes are missing labels. You can see the error here https://wave.webaim.org/report#/https://handbook.civicactions.com/en/latest/search.html?q=leave and screenshot:

Recommendation is to use aria-label to add the missing label. See https://www.w3.org/TR/WCAG20-TECHS/ARIA14.html for examples. I will submit a pull request to add the missing label.
I reported the same error for the Sphinx readthedocs theme: readthedocs/sphinx_rtd_theme#1379