refactor: resolve browser via env variables based on build rather than user agent (#27179)

Fixes https://github.com/facebook/react/issues/26911,
https://github.com/facebook/react/issues/26860.

Currently, we are parsing user agent string to determine which browser
is running the extension. This doesn't work well with custom user
agents, and sometimes when user turns on mobile dev mode in Firefox, we
stop resolving that this is a Firefox browser, extension starts to use
Chrome API's and fails to inject.

Changes:
Since we are building different extensions for all supported browsers
(Chrome, Firefox, Edge), we predefine env variables for browser
resolution, which are populated in a build step.