fix(collector): 기능 누락 3건 수정 — Discord 명령어/채팅/등록 중계

Gap 1: Discord→Extension 명령어 깨짐
  - bot.py: _write_command() 래퍼 — gateway.push_command()도 호출
  - main.py: bot.gateway 연결
  - 슬래시 명령어 + on_message 모두 _write_command 사용

Gap 2: Chat snapshot 미전달
  - collector.py: _forward_chat_snapshots_loop 추가

Gap 3: Session registration 미전달
  - collector.py: _forward_registrations_loop 추가

bot.py

@@ -180,6 +180,18 @@ class GravityBot(commands.Bot):
         self.session_category: discord.CategoryChannel | None = None
         self.guild: discord.Guild | None = None
         self.auto_approve_projects: set[str] = set()  # projects with auto-approve enabled
+        self.gateway = None  # Set by main.py in gateway mode
+
+    def _write_command(self, project: str, text: str, **kwargs):
+        """Write command to bridge AND push to gateway (if gateway mode)."""
+        self.bridge.write_command(project, text, **kwargs)
+        if self.gateway:
+            import time
+            self.gateway.push_command(project, {
+                "id": str(int(time.time() * 1000)),
+                "text": text,
+                "project_name": kwargs.get('project_name', project),
+            })
 
     @staticmethod
     def _make_channel_name(project_name: str) -> str:
@@ -202,7 +214,7 @@ class GravityBot(commands.Bot):
             if not project:
                 await interaction.response.send_message("⚠️ 프로젝트 채널이 아닙니다.", ephemeral=True)
                 return
-            self.bridge.write_command(project, "!stop", project_name=project)
+            self._write_command(project, "!stop", project_name=project)
             await interaction.response.send_message(
                 embed=discord.Embed(
                     title="⏹️ AI 작업 중지",
@@ -224,7 +236,7 @@ class GravityBot(commands.Bot):
             else:
                 self.auto_approve_projects.add(project)
                 enabled = True
-            self.bridge.write_command(project, f"!auto {'on' if enabled else 'off'}", project_name=project)
+            self._write_command(project, f"!auto {'on' if enabled else 'off'}", project_name=project)
             emoji = "🟢" if enabled else "🔴"
             await interaction.response.send_message(
                 embed=discord.Embed(
@@ -240,7 +252,7 @@ class GravityBot(commands.Bot):
             if not project:
                 await interaction.response.send_message("⚠️ 프로젝트 채널이 아닙니다.", ephemeral=True)
                 return
-            self.bridge.write_command(project, message, project_name=project)
+            self._write_command(project, message, project_name=project)
             await interaction.response.send_message(
                 embed=discord.Embed(
                     description=f"📨 → **{project}** IDE에 전달됨\n`{message[:100]}`",
@@ -754,7 +766,7 @@ class GravityBot(commands.Bot):
 
         # Special command: !stop — cancel AI work
         if text == "!stop":
-            self.bridge.write_command(project, "!stop", project_name=project)
+            self._write_command(project, "!stop", project_name=project)
             embed = discord.Embed(
                 title="⏹️ AI 작업 중지",
                 description=f"프로젝트: **{project}**\n중지 요청을 Extension에 전달했습니다.",
@@ -772,7 +784,7 @@ class GravityBot(commands.Bot):
             else:
                 self.auto_approve_projects.add(project)
                 enabled = True
-            self.bridge.write_command(project, f"!auto {'on' if enabled else 'off'}", project_name=project)
+            self._write_command(project, f"!auto {'on' if enabled else 'off'}", project_name=project)
             emoji = "🟢" if enabled else "🔴"
             mode = "자동 승인" if enabled else "수동 승인"
             embed = discord.Embed(
@@ -786,7 +798,7 @@ class GravityBot(commands.Bot):
 
         # General text relay — routed by project
         if text:
-            self.bridge.write_command(project, text, project_name=project)
+            self._write_command(project, text, project_name=project)
             await message.add_reaction("📨")
             embed = discord.Embed(
                 description=f"📨 → **{project}** IDE에 전달됨\n`{text[:100]}`",