[Task]: Optimize tests

Task to do:

Currently, many of our tests use a real browser that makes tests slow. We should re-architect tests to make sure we correct do unit tests: 1) tool handler tests that should just verify the outcome of the tool call on the context and response, they should use mocks 2) formatter tests should not use real McpContext 3) retain fewer tests using the real browser for high-level e2e tests.

Working on this task requires creating small PRs that can be easily reviewed to avoid loosing test coverage.