[test] consolidate the browser log test (#89601)
Filter out the extra logging from test env so we only assert on the
snapshot of forwarded logs
```
Snapshot name: `Terminal Logging (Webpack) App Router - Hydration Errors should show hydration errors with owner stack trace 1`
- Snapshot - 1
+ Received + 9
@@ -39,7 +39,15 @@
6 | <div>
> 7 | <p>{isClient ? 'client' : 'server'}</p>
| ^
8 | </div>
9 | )
- 10 | }
+ 10 | }
+
+
+ [12:36:48.104Z] Browser Log: received ws message {"type":"isrManifest","data":{"/hydration-error":true}}
+
+ [12:36:48.104Z] Browser Log: Next.js page already hydrated
+
+ [12:36:48.109Z] Hydration complete for http://localhost:46145/hydration-error
"
at Object.toMatchInlineSnapshot (/root/actions-runner/_work/next.js/next.js/test/development/browser-logs/browser-logs.test.ts:317:33)
at runNextTicks (node:internal/process/task_queues:60:5)
at processImmediate (node:internal/timers:449:9)
at process.callbackTrampoline (node:internal/async_hooks:130:17)
```
