Fix E2E test flakiness

[sidvishnoi]

As discovered in #864 (comment), #864 (comment) and #864 (comment).

[sidvishnoi]

After numerous failed attempts today trying to clear extension state after each file, it's best to isolate tests for now, and create new browser for each test (not per file) until Playwright supports not reusing worker or cleanup per file.
This would make tests much slower, but at least they won't be flaky.

Another alternative would be to let go of fixtures and setup & teardown at top level manually, but that would be more trouble. Once Playwright has file level scope, we can simply replace scope in fixtures then.

[sidvishnoi]

For performance with isolation, we can then increase parallelism with more workers and enabling fullyParallel.