[1.x] fix(testing): use cookie for testing authentication

[huoxin233]

Fixes #3834

Changes proposed in this pull request:

Backport fix #3924 to 1.x

Was writing a test for a custom route but keep failing, realized that the issue is not fixed in 1.x

Reviewers should focus on:

Screenshot

Necessity

• Has the problem that is being solved here been clearly explained?
• If applicable, have various options for solving this problem been considered?
• For core PRs, does this need to be in core, or could it be in an extension?
• Are we willing to maintain this for years / potentially forever?

Confirmed

• Frontend changes: tested on a local Flarum installation.
• Backend changes: tests are green (run composer test).
• Core developer confirmed locally this works as intended.
• Tests have been added, or are not appropriate here.

Required changes:

• Related documentation PR: (Remove if irrelevant)