Figure out best way to reuse browser instances

[HaoK]

As part of the logging changes in #30907 each test has its own playwright fixture, should go back to a single shared fixture, or at least figure out what's the ideal reuse of browser instances (today we create new instances always)

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We're moving this issue to the Next sprint planning milestone for future evaluation / consideration. Because it's not immediately obvious that this is a bug in our framework, we would like to keep this around to collect more feedback, which can later help us determine the impact of it. We will re-evaluate this issue, during our next planning meeting(s).
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