Add e2e tests

[olaservo]

Motivation and Context

Opening as a draft for feedback on this general approach. There's a few configs that need to get adjusted or cleaned up here and obviously the oauth part is still mostly // TODO.

Will plan to update to include Streamable Http once we can import the latest changes from the published package.

How Has This Been Tested?

To run these tests I've been doing the following:

1. In one terminal, run Inspector locally

2. In another terminal, run one of the transport-specific test commands, eg:

cd client
npm run test:e2e:sse
# or
npm run test:e2e:stdio

Breaking Changes

None

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• Documentation update

Checklist

• I have read the MCP Documentation
• My code follows the repository's style guidelines
• New and existing tests pass locally
• I have added appropriate error handling
• I have added or updated documentation as needed

[olaservo]

Some of these dependency updates are probably from a previous attempt on same branch - main ones to pay attention to are importing server-everything and adding Playwright to dev dependences.