Migrate App Mode Tests to Default Playwright Structure

[vyncent-t]

Description

I am currently working on migrating the existing Playwright tests for app mode into the default Playwright structure used in our project. The goal is to unify the test structure for both web and app modes, ensuring consistent and maintainable end-to-end testing across environments. This migration will not only align with Playwright’s best practices but will make it easier to develop and run tests for us.

I am also working on a way to get the current tests running across multiple environments with less friction.

[vyncent-t]

This issue is no longer needed, as mentioned in issue #2183