fix(lsp): broken-server recovery + config source attribution

Two issues found by decompiling the running dispatch-server binary
(handoff from a ruby-lsp setup in raylib-jamstack):

Issue 2 (blocker): a failed LSP server was "broken" FOREVER — the
manager's broken set was cleared only in shutdownAll(), so a server
that failed (bad env, missing binary, or a since-fixed config) stayed
state:"error" for the whole process. For an agent running *inside*
dispatch the only recovery (server restart) kills its own session.
Now a broken server self-heals when its resolved config changes since
it was marked broken (discrete event → no retry storm), with a bounded
backoff for transient failures.

Issue 1: .dispatch/lsp.json silently shadowed opencode.json's lsp key
with no warning and no source attribution. Now: shadow warning via
host.logger when both declare lsp; configSource populated on status
(.dispatch/lsp.json / opencode.json / built-in); spawn-failure error
strings name the config source.

Contract: additive configSource?: string on LspServerInfo
(@dispatch/transport-contract 0.20.0→0.21.0). transport-http passes it
through to the wire (was a field-by-field map that dropped it — CR
resolved by the transport-http owner).

tsc -b EXIT 0, biome clean, 1443 vitest pass.

2 files changed, 66 insertions, 0 deletions

diff --git a/packages/transport-http/src/app.test.ts b/packages/transport-http/src/app.test.ts
index 153a63a..a84fa44 100644
--- a/packages/transport-http/src/app.test.ts
+++ b/packages/transport-http/src/app.test.ts
@@ -364,6 +364,7 @@ function createFakeLspService(
 		readonly extensions: readonly string[];
 		readonly state: "connected" | "starting" | "error" | "not-started";
 		readonly error?: string;
+		readonly configSource?: string;
 	}[] = [],
 ): LspService {
 	return {
@@ -381,6 +382,7 @@ function createCapturingLspService(
 		readonly extensions: readonly string[];
 		readonly state: "connected" | "starting" | "error" | "not-started";
 		readonly error?: string;
+		readonly configSource?: string;
 	}[] = [],
 ): LspService & { readonly statusCalls: readonly string[] } {
 	const calls: string[] = [];
@@ -2317,6 +2319,69 @@ describe("GET /conversations/:id/lsp", () => {
 		expect(body.servers).toHaveLength(1);
 		expect(body.servers[0]?.id).toBe("typescript");
 	});
+
+	it("GET /conversations/:id/lsp: configSource passes through to the wire", async () => {
+		const cwdStore = new Map<string, string>([["conv1", "/home/user/project"]]);
+		const store = createFakeConversationStore(new Map(), new Map(), cwdStore);
+		// Case 1: configSource is defined → reaches the wire verbatim.
+		const lspWithSource = createFakeLspService([
+			{
+				id: "typescript",
+				name: "TypeScript",
+				root: "/home/user/project",
+				extensions: [".ts", ".tsx"],
+				state: "connected" as const,
+				configSource: ".dispatch/lsp.json",
+			},
+		]);
+		const appWithSource = createApp({
+			conversationStore: store,
+			orchestrator: createFakeOrchestrator([]),
+			credentialStore: createFakeCredentialStore([]),
+			lspService: lspWithSource,
+			logger: noopLogger,
+		});
+		const resWithSource = await appWithSource.request("/conversations/conv1/lsp");
+		expect(resWithSource.status).toBe(200);
+		const bodyWithSource = (await resWithSource.json()) as {
+			conversationId: string;
+			cwd: string | null;
+			servers: readonly {
+				readonly id: string;
+				readonly configSource?: string;
+			}[];
+		};
+		expect(bodyWithSource.servers[0]?.configSource).toBe(".dispatch/lsp.json");
+
+		// Case 2: configSource is undefined → the field is OMITTED from the
+		// response (proves exactOptionalPropertyTypes is respected — never
+		// stamping `undefined` onto the wire object).
+		const lspWithoutSource = createFakeLspService([
+			{
+				id: "typescript",
+				name: "TypeScript",
+				root: "/home/user/project",
+				extensions: [".ts", ".tsx"],
+				state: "connected" as const,
+			},
+		]);
+		const appWithoutSource = createApp({
+			conversationStore: store,
+			orchestrator: createFakeOrchestrator([]),
+			credentialStore: createFakeCredentialStore([]),
+			lspService: lspWithoutSource,
+			logger: noopLogger,
+		});
+		const resWithoutSource = await appWithoutSource.request("/conversations/conv1/lsp");
+		expect(resWithoutSource.status).toBe(200);
+		const bodyWithoutSource = (await resWithoutSource.json()) as {
+			conversationId: string;
+			cwd: string | null;
+			servers: readonly Record<string, unknown>[];
+		};
+		expect(bodyWithoutSource.servers).toHaveLength(1);
+		expect(bodyWithoutSource.servers[0]).not.toHaveProperty("configSource");
+	});
 });
 
 describe("POST /chat reasoningEffort", () => {
diff --git a/packages/transport-http/src/app.ts b/packages/transport-http/src/app.ts
index 7fdbb00..2a98ea0 100644
--- a/packages/transport-http/src/app.ts
+++ b/packages/transport-http/src/app.ts
@@ -703,6 +703,7 @@ export function createApp(opts: CreateServerOptions): Hono {
 					extensions: s.extensions,
 					state: s.state,
 					...(s.error !== undefined ? { error: s.error } : {}),
+					...(s.configSource !== undefined ? { configSource: s.configSource } : {}),
 				};
 				return info;
 			});