GOSC-E2E-3: Add signup test, with test db

[Geethegreat]

Issue:

Fixes #

Demo:

e2e-flow-3.mp4

Changes:

• Added a Playwright E2E test covering user registration with username, email, and password.
• Verified that newly registered users are authenticated and redirected successfully after signup.
• Added a dedicated E2E test database configuration to isolate test data from development data.
• Added a Playwright globalTeardown step to clean up the test database after execution.
• Updated Playwright configuration to support E2E database lifecycle management.

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