feat(mcp): declare experimental.claude/channel capability for push UX

Without this capability declaration in the initialize handshake,
Claude Code's MCP client receives our notifications/claude/channel
emissions but silently drops them — they never become inline
<channel> tags in the conversation. The push-UX bridge added in
PR #2433 ships, fires, and is invisible.

This was anticipated as a failure mode in #2444 §2 ("Notification
arrives but Claude Code doesn't surface it — host doesn't recognize
the method"), and confirmed live in this session: a canvas chat
"hi" landed in the inbox queue (inbox_peek returned it) but never
woke the agent until inbox_peek was called by hand.

The contract matches molecule-mcp-claude-channel/server.ts:374
where the bun bridge declares the same experimental flag.

Refactor: extracted _build_initialize_result() so the handshake
shape is unit-testable. Pure function, no behavioral change beyond
adding the experimental capability to the result.

Tests: 3 new pins on the initialize result (capability presence,
tools-still-there, protocolVersion stable). Closes the live-
verification gap §2 of #2444.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

workspace/a2a_mcp_server.py

@@ -149,6 +149,30 @@ async def handle_tool_call(name: str, arguments: dict) -> str:
 _CHANNEL_NOTIFICATION_METHOD = "notifications/claude/channel"
 
 
+def _build_initialize_result() -> dict:
+    """MCP initialize handshake result.
+
+    The ``experimental.claude/channel`` capability declaration is what
+    tells Claude Code's MCP client to route our
+    ``notifications/claude/channel`` emissions as conversation
+    interrupts (push UX). Without it the notification arrives over the
+    wire but is silently dropped instead of becoming a ``<channel>``
+    tag in the next agent turn — matching the
+    "Notification arrives but Claude Code doesn't surface it" failure
+    mode anticipated in molecule-core#2444. Mirrors the contract
+    declared by the molecule-mcp-claude-channel bun bridge
+    (server.ts:374).
+    """
+    return {
+        "protocolVersion": "2024-11-05",
+        "capabilities": {
+            "tools": {"listChanged": False},
+            "experimental": {"claude/channel": {}},
+        },
+        "serverInfo": {"name": "a2a-delegation", "version": "1.0.0"},
+    }
+
+
 def _build_channel_notification(msg: dict) -> dict:
     """Transform an ``InboxMessage.to_dict()`` into the MCP notification
     envelope expected by Claude Code's channel-bridge contract.
@@ -246,11 +270,7 @@ async def main():  # pragma: no cover
                     await write_response({
                         "jsonrpc": "2.0",
                         "id": req_id,
-                        "result": {
-                            "protocolVersion": "2024-11-05",
-                            "capabilities": {"tools": {"listChanged": False}},
-                            "serverInfo": {"name": "a2a-delegation", "version": "1.0.0"},
-                        },
+                        "result": _build_initialize_result(),
                     })
 
                 elif method == "notifications/initialized":

workspace/tests/test_a2a_mcp_server.py

@@ -237,3 +237,44 @@ def test_build_channel_notification_handles_missing_fields_gracefully():
     assert meta["activity_id"] == ""
     assert meta["peer_id"] == ""
     assert meta["kind"] == ""
+
+
+# ============== initialize handshake — capability declaration ==============
+# Without `experimental.claude/channel`, Claude Code's MCP client drops
+# our notifications/claude/channel emissions instead of routing them as
+# inline conversation interrupts. Anticipated as a failure mode in
+# molecule-core#2444 ("notification arrives but Claude Code doesn't
+# surface it"). Pin the declaration here so a refactor of
+# _build_initialize_result can't silently strip the flag.
+
+
+def test_initialize_declares_experimental_claude_channel_capability():
+    """Without this capability the push-UX bridge ships, the
+    notifications fire, and nothing happens in the host — silent. This
+    is the contract that flips Claude Code's routing on."""
+    from a2a_mcp_server import _build_initialize_result
+
+    result = _build_initialize_result()
+    experimental = result["capabilities"].get("experimental", {})
+
+    assert "claude/channel" in experimental, (
+        "experimental.claude/channel capability is required for Claude "
+        "Code to surface our notifications/claude/channel emissions as "
+        "conversation interrupts (issue #2444 §2). Removing this would "
+        "regress live push UX while leaving every unit test green."
+    )
+
+
+def test_initialize_keeps_tools_capability():
+    """Pin the tools capability too — losing it would break tools/list."""
+    from a2a_mcp_server import _build_initialize_result
+
+    assert "tools" in _build_initialize_result()["capabilities"]
+
+
+def test_initialize_protocol_version_is_pinned():
+    """MCP protocol version is part of the handshake contract; bumping
+    it changes what fields the host expects."""
+    from a2a_mcp_server import _build_initialize_result
+
+    assert _build_initialize_result()["protocolVersion"] == "2024-11-05"