Many websites focus the search box when the forward slash / key is pressed.

For example:

• Furo theme https://pradyunsg.me/furo/quickstart/
• PyPI https://pypi.org/project/python-docs-theme/
• GitHub Focus search box when pressing slash #130
• YouTube https://www.youtube.com/watch?v=nMekFX2CDVk
• Discourse https://discuss.python.org/

Here's how PyPI implemented it: pypi/warehouse#10395