Write example integration tests for web

[ti2ger92]

Write an integration test (in the tests/e2e folder of the web repo. e2e = end to end). Test a small, simple, and core feature in at least 3 ways; verify the general case, plus a couple edge cases.
Example: write 3 integration tests for the student signup process > test the ability to successfully create a new student account > test the inability to sign up with an existing student account's email > test the inability to sign up with an invalid password

Make sure to research and implement all current best practices, because this will inform future integration tests