feat: Review and increase E2E test coverage

[lornakelly]

Description

Review existing Playwright end-to-end tests and expand coverage where needed.

Motivation

Strengthen confidence in end-to-end behaviour and reduce the risk of regressions in critical user interactions.

Proposed Implementation

No response

Definition of Done

• Implementation: Fully implemented according to the Serverless Workflow spec.
• Unit Tests: Comprehensive unit tests are included and passing.
• Integration Tests: Verified within the monorepo and target environments (Web/VS Code).
• Documentation: Updated README.md, ADRs, or official docs.
• Performance: No significant regression in editor responsiveness.
• Accessibility: UI changes comply with accessibility standards.