[test] Deflake `browser-log-forwarding verbose level` test suite (#89324)
[flakiness
metric](https://app.datadoghq.com/ci/test/runs?query=test_level%3Atest%20%40git.repository.id%3A%22github.com%2Fvercel%2Fnext.js%22%20%40test.name%3A%22browser-log-forwarding%20verbose%20level%20should%20forward%20all%20logs%20to%20terminal%22%20%40test.type%3A%22nextjs%22%20%40test.status%3Afail&agg_m=count&agg_m_source=base&agg_t=count&fromUser=false&index=citest&start=1769207121512&end=1769811921512&paused=false)
The test frequently failed because it snapshot-asserted on the forwarded
browser logs before the final debug message was forwarded. This is
because the initial assertion inside the `retry` block would pass
because it falsely matched the debug message inside the error code frame
(line 11):
```
[browser] browser error: this is an error message
at Page.useEffect (app/page.tsx:10:13)
8 | console.info('browser info: this is an info message')
9 | console.warn('browser warn: this is a warning message')
> 10 | console.error('browser error: this is an error message')
| ^
11 | console.debug('browser debug: this is a debug message')
12 | }, [])
13 | (app/page.tsx:10:13)
```
By adding the `[browser] ` prefix to all expected log messages, we
ensure that the test only passes when the actual log messages are
forwarded, and not when they appear inside code frames.
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