Browser extension styles conflict with GitHub

Created by: taras-yemets

• Browser extension version: main branch in its current state. bext/release branch and thus latest browser extension version (22.4.7.1712) are not affected.
• Platform information: Sourcegraph browser extension on GitHub.

Steps to reproduce:

1. Open any GitHub page with the latest browser extension version (22.4.7.1712) or with the browser extension disabled and pay attention to the search dropdown and buttons styles.
2. Pull the latest main branch and run the browser extension locally with sg run bext.
3. Switch to use the local browser extension build in the browser and reload the GitHub page. Pay attention to how search dropdown, buttons, and other styles were affected.

Expected behavior:

GitHub styles are not affected by the browser extension (check out search dropdown items in red and buttons in yellow).

Actual behavior:

Mentioned elements on the GitHub page have broken styles.