Update Automated Testing Documentation

The [Automated Testing README](https://github.com/Automattic/jetpack/blob/trunk/docs/automated-testing.md) has out-of-date links and doesn't provide the key info needed: **how to run the tests.**

This info is included in other places though. Linking to the appropriate location in the [Development Environment](https://github.com/Automattic/jetpack/blob/trunk/docs/development-environment.md#unit-testing) README would be helpful, but I think it would be best to move the instructions into the Automated Testing README. That feels more appropriate than including the instructions in Development Environment, as this topic is more related to Automated Testing than Development Environment.

## Tasks
- [ ] Link to or provide instructions on how to run automated tests within the [Automated Testing README](https://github.com/Automattic/jetpack/blob/trunk/docs/automated-testing.md)
- [ ] Fix minor grammatical errors
- [ ] Expand upon or remove, "Note: Jetpack monorepo is using a bit different code style to one that used in documentation examples." What is different? Is it important to know? If not, let's remove it.
- [ ] Update [PHPUnit instructions](https://github.com/Automattic/jetpack/blob/trunk/docs/development-environment.md#php-unit-tests) and remove the "This section is in need of update! Changes to how WordPress sets up its tests mean that a global version of phpunit is no longer provided." message