[wpt][fetch-api] Don't persist cookie in `cors-filtering.sub.any.js`

... since only response headers are tested, not the `Cookie` request
header. This stops cookie pollution causing spurious failures in other
tests if the same browser is used (e.g., [0]).

Also, remove some `Test.done()`s that aren't necessary for
`promise_test()`s.

[0]: https://wpt.fyi/results/fetch/api/credentials/cookies.any.html?run_id=5204090552582144

Bug: None
Change-Id: Ie75af268052f32acf96c00c9b3948a5ee4cf3019
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5838015
Reviewed-by: Adam Rice <ricea@chromium.org>
Commit-Queue: Jonathan Lee <jonathanjlee@google.com>
Cr-Commit-Position: refs/heads/main@{#1352807}