GSOC-E2E-5: Add unauthenticated-to-authenticated user workflow

[Geethegreat]

Issue:

Fixes #

Demo:

e2e-flow-5.mp4

Changes:

• Added a Playwright E2E test covering the unauthenticated-to-authenticated user workflow.
  • Verifies that a guest user can write and execute a sketch before creating an account.
  • Confirms that attempting to save as an unauthenticated user prompts account creation.
  • Completes the signup flow through the UI using a unique test account.
  • Verifies that the authenticated session is established successfully after signup.
  • Ensures the sketch persists and can be executed successfully after the user becomes authenticated.

I have verified that this pull request:

• has no linting errors (npm run lint)
• has no test errors (npm run test)
• has no typecheck errors (npm run typecheck)
• is from a uniquely-named feature branch and is up to date with the develop branch.
• is descriptively named and links to an issue number, i.e. Fixes #123
• meets the standards outlined in the accessibility guidelines