test: reorganize helpers into shared/e2e/int subdirectories (#15479)

Clean up `test/helpers/` folder structure in preparation for upcoming
fixtures support.

Previously, all helper files were in a flat structure making it hard to
distinguish between shared utilities and <e2e/int>-specific helpers.
Some were part of the `test/helpers/e2e` folder, some were just floating
at the top-level of the `test/helpers` _folder_, some were stuffed into
`test/helpers.ts` _file_.

New structure:

- `helpers/shared/` - Common utilities (adminUrlUtil, initPayloadInt,
REST clients, etc.)
- `helpers/e2e/` - Playwright/e2e test utilities
- `helpers/int/` - Integration test utilities

This PR also removes some previously unused files. We still had mock
files sitting around from our 2.x webpack bundler magic days.