fix(ai-checker): keep CLI stderr out of the verdict and surface it on failure

AiCheckerBase spawned the check with `> out 2>&1`, so anything the Claude CLI
wrote to stderr landed inside the same file the verdict parser reads. A CLI that
failed to start (corrupt settings, missing auth) produced either an empty verdict
or an unparseable one, and the actual cause was destroyed on the way through —
the user saw only "Empty output from AI idle check".

stderr now goes to its own temp file. When output is empty or the verdict cannot
be parsed, the first 200 characters of stderr are appended to the error message.
The file is cleaned up alongside the existing temp files, including on the error
paths.

Two tests, both failing on master:
  expected 'export PATH="…' to contain ' 2> "'
  expected 'Empty output from AI idle check' to contain 'Claude CLI failed to load settings'

src/ai-checker-base.ts

@@ -135,6 +135,7 @@ export abstract class AiCheckerBase<
   // Active check state
   protected checkMuxName: string | null = null;
   protected checkTempFile: string | null = null;
+  protected checkStderrFile: string | null = null;
   protected checkPromptFile: string | null = null;
   protected checkPollTimer: NodeJS.Timeout | null = null;
   protected checkTimeoutTimer: NodeJS.Timeout | null = null;
@@ -376,6 +377,7 @@ export abstract class AiCheckerBase<
     const shortId = this.sessionId.slice(0, 8);
     const timestamp = Date.now();
     this.checkTempFile = join(tmpdir(), `${this.tempFilePrefix}-${shortId}-${timestamp}.txt`);
+    this.checkStderrFile = join(tmpdir(), `${this.tempFilePrefix}-stderr-${shortId}-${timestamp}.txt`);
     this.checkPromptFile = join(tmpdir(), `${this.tempFilePrefix}-prompt-${shortId}-${timestamp}.txt`);
     this.checkMuxName = `${this.muxNamePrefix}${shortId}`;
 
@@ -386,6 +388,7 @@ export abstract class AiCheckerBase<
 
     // Ensure output temp file exists (empty) so we can poll it
     writeFileSync(this.checkTempFile, '');
+    writeFileSync(this.checkStderrFile, '');
 
     // Write prompt to file to avoid E2BIG error (argument list too long)
     // The prompt can be 16KB+ which exceeds shell argument limits
@@ -396,7 +399,7 @@ export abstract class AiCheckerBase<
     const modelArg = `--model "${this.config.model.replace(/"/g, '\\"')}"`;
     const augmentedPath = getAugmentedPath();
     const claudeCmd = `cat "${this.checkPromptFile}" | claude -p ${modelArg} --output-format text`;
-    const fullCmd = `export PATH="${augmentedPath}"; ${claudeCmd} > "${this.checkTempFile}" 2>&1; echo "${this.doneMarker}" >> "${this.checkTempFile}"; rm -f "${this.checkPromptFile}"`;
+    const fullCmd = `export PATH="${augmentedPath}"; ${claudeCmd} > "${this.checkTempFile}" 2> "${this.checkStderrFile}"; echo "${this.doneMarker}" >> "${this.checkTempFile}"; rm -f "${this.checkPromptFile}"`;
 
     // Spawn tmux session
     try {
@@ -461,18 +464,32 @@ export abstract class AiCheckerBase<
     const output = content.replace(this.doneMarker, '').trim();
 
     if (!output) {
-      return this.createErrorResult(`Empty output from ${this.checkDescription}`, durationMs);
+      const stderr = this.readStderrDiagnostic();
+      const detail = stderr ? `: ${stderr}` : '';
+      return this.createErrorResult(`Empty output from ${this.checkDescription}${detail}`, durationMs);
     }
 
     // Delegate to subclass for verdict parsing
     const parsed = this.parseVerdict(output);
     if (!parsed) {
-      return this.createErrorResult(`Could not parse verdict from: "${output.substring(0, 100)}"`, durationMs);
+      const stderr = this.readStderrDiagnostic();
+      const detail = stderr ? `; stderr: "${stderr}"` : '';
+      return this.createErrorResult(`Could not parse verdict from: "${output.substring(0, 100)}"${detail}`, durationMs);
     }
 
     return this.createResult(parsed.verdict, parsed.reasoning, durationMs);
   }
 
+  private readStderrDiagnostic(): string {
+    if (!this.checkStderrFile || !existsSync(this.checkStderrFile)) return '';
+
+    try {
+      return readFileSync(this.checkStderrFile, 'utf-8').trim().substring(0, 200);
+    } catch {
+      return '';
+    }
+  }
+
   private cleanupCheck(): void {
     // Clear poll timer
     if (this.checkPollTimer) {
@@ -509,6 +526,17 @@ export abstract class AiCheckerBase<
       this.checkTempFile = null;
     }
 
+    if (this.checkStderrFile) {
+      try {
+        if (existsSync(this.checkStderrFile)) {
+          unlinkSync(this.checkStderrFile);
+        }
+      } catch {
+        // Best effort cleanup
+      }
+      this.checkStderrFile = null;
+    }
+
     if (this.checkPromptFile) {
       try {
         if (existsSync(this.checkPromptFile)) {