fix: pipe Next.js server stdout/stderr to debug log file

[thesandlord]

Description

Refs: Related to fern-api/fern-platform#9752

Previously, the Next.js standalone server's stdout/stderr was only sent to context.logger.debug(), which does not write to the ~/.fern/logs/*.debug.log file. This made it impossible to diagnose server-side errors (e.g. 500 responses, module resolution failures) from the debug log — only CLI-level structured events (reload, validation, memory) appeared there.

Changes Made

• Added DebugLogger.logServerOutput(stream, text) method that writes structured JSON entries with source: "nextjs-server" and appropriate log levels ("error" for stderr, "debug" for stdout)
• Wired up all four server output channels in runAppPreviewServer.ts to write to the debug log:
  • stdout data (the checkReady handler)
  • stderr data
  • Process error events
  • Process exit events
• Added "nextjs_server_output" to the CliMetricEvent type union

All calls use void (fire-and-forget) to avoid blocking server operation, matching the existing pattern for other debug logger calls.

Review Checklist

• "nextjs_server_output" was added to CliMetricEvent.type, but logServerOutput writes directly via writeEntry rather than going through logCliMetric — the type union addition is not strictly necessary. Confirm this is acceptable or should be removed.
• Verify that high-volume stdout (e.g. during SSR of many pages) won't cause excessive disk writes or performance issues via the fire-and-forget appendFile calls.

Testing

• Manual testing not feasible in this environment (requires Windows + fern docs dev)
• Lint passes (pnpm run check)
• No unit tests added — this is a logging-only change with no behavioral impact on the server itself

Link to Devin session: https://app.devin.ai/sessions/384de2d2e741453fa07377d662b6e2c2
Requested by: @thesandlord

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