dev: add Playwright as a testing tool

[mastercactapus]

What problem would you like to solve? Please describe:

• Flaky Cypress selector chains
• Inability to test popup links & separate servers/hosts (e.g., oauth flows)
• Cypress upgrades frequently break tests & require manual updates
• Layout of tests & locations isn't documented
• Cypress test code needs to be built/bundled to run in the browser
• Inability to use things like async/await

Describe the solution you'd like:

• Move smoketests to tests/smoketest
• Create tests/integration for playwright tests
• Add test-integration and start-integration make targets (prod-mode only)
• Add EMAIL contact method as first test
• Add test-integration target to build-all script in CI

Describe alternatives you've considered:
The current setup works for what it can do, and there are workarounds like setting up reverse proxy routes to get around some of Cypress's limitations; but it all adds complexity, time, and maintenance cost.

Playwright was evaluated and has a preferable setup, better integration with existing IDEs, and more flexibility to test multiple tabs/windows & concurrently run tests.

Additional context: