feat: add streaming responses to API and CLI

Add real-time streaming support for agent responses using Server-Sent
Events (SSE). Responses now appear as they're generated instead of
waiting for completion.

- Add run_stream method to BaseAgent and ExploreAgentImpl
- Add /agents/stream SSE endpoint to API router
- Add run_agent_stream method to CLI client
- Add --stream flag to chat and explore commands (enabled by default)
- Use --no-stream for batch mode with spinner

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

webber-api/src/domains/agents/explore/agent.py

@@ -5,6 +5,7 @@ Fast codebase exploration with read-only tools.
 Uses sanitized Ollama provider for reliable tool calling.
 """
 import os
+from collections.abc import AsyncIterator
 from dataclasses import dataclass
 from typing import Any
 
@@ -113,6 +114,34 @@ class ExploreAgentImpl(BaseAgent):
                 raise
 
 
+    async def run_stream(
+        self,
+        prompt: str,
+        working_dir: str | None = None,
+        allowed_paths: list[str] | None = None,
+        **kwargs: Any
+    ) -> AsyncIterator[str]:
+        """
+        Run the explore agent with streaming output.
+
+        Yields text chunks as they become available.
+        """
+        ctx = ExploreContext(
+            working_dir=working_dir or os.getcwd(),
+            allowed_paths=allowed_paths or self._settings.effective_allowed_paths,
+            timeout_seconds=self._settings.tool_timeout_seconds,
+        )
+
+        async with trace_span("explore_agent_stream"):
+            try:
+                async with self.agent.run_stream(prompt, deps=ctx) as result:
+                    async for chunk in result.stream_text():
+                        yield chunk
+            except Exception as e:
+                logger.exception(f"Explore agent stream error: {e}")
+                raise
+
+
 # Create and register the singleton instance
 explore_agent = ExploreAgentImpl()
 register_agent(explore_agent)
@@ -125,3 +154,13 @@ async def explore(
 ) -> str:
     """Run exploration query."""
     return await explore_agent.run(prompt, working_dir=working_dir, **kwargs)
+
+
+async def explore_stream(
+    prompt: str,
+    working_dir: str | None = None,
+    **kwargs: Any
+) -> AsyncIterator[str]:
+    """Run exploration query with streaming."""
+    async for chunk in explore_agent.run_stream(prompt, working_dir=working_dir, **kwargs):
+        yield chunk