feat(commands): Add agentmail integration to /sync, add missing skill dirs

/sync now checks for unread mail at session bootstrap (Step 5), shows
Mail section with preview, and suggests agentmail read in Next Steps.
Degrades silently if agentmail is not installed. Also adds missing
references/ and assets/ directories to agentmail skill per conventions.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

commands/sync.md

@@ -148,7 +148,20 @@ git log -1 --format="%h %s" 2>/dev/null
 - `wc -l` in Git Bash = count lines (CORRECT)
 - Git Bash understands `2>/dev/null` but NOT `2>nul`
 
-### Step 5: Acknowledge Memory
+### Step 5: Check Mail
+
+Check for unread agentmail messages using the globally installed script:
+
+```bash
+bash "$HOME/.claude/agentmail/mail-db.sh" status 2>/dev/null
+bash "$HOME/.claude/agentmail/mail-db.sh" unread 2>/dev/null
+```
+
+- If the script doesn't exist or returns no unread, skip silently
+- If unread messages exist, show count and preview in the output Mail section
+- Do NOT auto-mark messages as read - just show what's waiting
+
+### Step 6: Acknowledge Memory
 
 MEMORY.md is auto-loaded into the system prompt by Claude Code - do NOT re-read the file.
 Instead, check your system prompt for the memory content you already have, and surface it:
@@ -158,7 +171,7 @@ Instead, check your system prompt for the memory content you already have, and s
 
 This costs zero extra tokens while confirming the safety net is working.
 
-### Step 6: Output
+### Step 7: Output
 
 Format and display unified status.
 
@@ -223,6 +236,18 @@ Note: PR row only shown when pr_number/pr_url are present in saved state.
 Note: MEMORY.md is auto-loaded into the system prompt. This section surfaces
 what's already in context - no file read needed.
 
+## Mail
+
+[If agentmail is installed and has unread messages:]
+3 unread messages:
+  From: some-api  |  Auth endpoints ready
+  From: frontend  |  Need updated types
+  From: infra     |  Deploy complete
+
+Run `agentmail read` to read.
+
+[If no unread messages or agentmail not installed: omit this section entirely]
+
 ## Quick Reference
 
 | Category | Items |
@@ -233,10 +258,11 @@ what's already in context - no file read needed.
 
 ## Next Steps
 
-1. **Continue**: Fix callback URL handling
-2. **Check diff**: /sync --diff to see changes since save
-3. **Resume conversation**: `claude --resume abc123...` (when session_id present)
-4. **PR context**: `claude --from-pr 42` (when PR is linked)
+1. **Read mail**: N unread messages - `agentmail read` (when unread mail exists)
+2. **Continue**: Fix callback URL handling
+3. **Check diff**: /sync --diff to see changes since save
+4. **Resume conversation**: `claude --resume abc123...` (when session_id present)
+5. **PR context**: `claude --from-pr 42` (when PR is linked)
 ```
 
 Note: Next Steps items 3-4 are only shown when the corresponding data exists in saved state.
@@ -262,13 +288,15 @@ Project Synced: [project-name]
 | **Plan** | No active plan |
 | **Saved State** | None |
 | **Memory** | [summary of MEMORY.md content, or "Empty"] |
+| **Mail** | [N unread, or omit row if none/not installed] |
 | **Git** | [branch], [N] uncommitted |
 
 ## Next Steps
 
-1. **Ready for new task** - No pending work detected
-2. **Create a plan** - Use native /plan for implementation planning
-3. **Save before leaving** - /save "notes" to persist state
+1. **Read mail**: N unread messages - `agentmail read` (when unread mail exists)
+2. **Ready for new task** - No pending work detected
+3. **Create a plan** - Use native /plan for implementation planning
+4. **Save before leaving** - /save "notes" to persist state
 ```
 
 ---
@@ -421,6 +449,10 @@ Status
 
 [Summary of MEMORY.md content, or "Empty"]
 
+## Mail
+
+[N unread messages with preview, or omit if none/not installed]
+
 ## Git
 
 | Field | Value |