Update integration tests

[psilabs-dev]

• compare: psilabs-dev/aio-lanraragi@e50968c...4c5ffe9
• PR: Client v0.1.15, Tests v0.1.16 psilabs-dev/aio-lanraragi#163

No new tests planned atm, instead I've stabilized the existing test cases and make conditions stricter.

• Redis/docker connections will be explicitly closed on teardown when applicable.

The following updates apply to all Playwright UI tests:

• All tests now explicitly create a browser context, and explicitly close context/browser within the scope of a test case.
• All tests assert no errors when checking browser network inspector. This means that a UI test case will fail if the network inspector finds any LRR-side status code that isn't sub-400 or 401. Non-LRR origin URLs are excluded (e.g. Github rate limit errors will not trigger test case failure). This is a stricter client-side condition than expecting no server-side error logs, as 4xx validation errors and silent, server-side error responses will fail the test case. This will address a subset of upcoming OpenAPI integration testing failures, including the missing "/search" endpoint issue that escaped testing from earlier.

Log health assertions are occasionally capturing Shinobu error logs ("giving up adding it to the filesystem"); this is an existing race condition which can be ignored, or we can suppress it in the future test-side or LRR-side.