Use `b` in watch mode to restart the browser server

Clear and concise description of the problem

When running in watch mode, sometimes the browser instance is in a bad state, causing all browser tests to time out.

I have to quit the watch mode and restart.

Suggested solution

Instead of having b to do press b to start the browser server if not started yet,
use it to restart the browser instance(s) so we don't need to restart watch mode.

Alternative

Automatically detect dead browser and restart. To do that need to add a special heartbeat command to ensure the browser is still in good shape. However, determine what does "good shape" means could be challenging.

Additional context

No response

Validations

• Follow our Code of Conduct
• Read the Contributing Guidelines.
• Read the docs.
• Check that there isn't already an issue that request the same feature to avoid creating a duplicate.

The issue names no files, tests, or entry points. Start by tracing watch-mode handling of the b key and the browser server lifecycle; done means pressing b restarts the browser instance or instances without restarting watch mode, with coverage for the restart behavior.