fix(cli): treat omitted sentence-transformers base_url as managed daemon

After PR #184 and #192 moved managed-embeddings URL resolution to the
CLI project boundary and made `ktx setup` persist `ktx.yaml` without a
`base_url`, the status command still treated the empty value as
misconfiguration and printed "no base_url configured", dragging the
verdict down to "Partially ready — embedding credentials missing".

Update `buildEmbeddingsStatus` to recognize the managed-daemon
convention and report it as ok. Add a `status-project.test.ts` covering
the explicit-url, omitted, empty-string, and openai-missing-key paths.

packages/cli/src/status-project.test.ts

@@ -0,0 +1,126 @@
+import { describe, expect, it } from 'vitest';
+import { buildDefaultKtxProjectConfig, type KtxLocalProject, type KtxProjectConfig } from '@ktx/context/project';
+import { buildProjectStatus } from './status-project.js';
+
+function projectWithConfig(config: KtxProjectConfig): KtxLocalProject {
+  return {
+    projectDir: '/work/proj',
+    configPath: '/work/proj/ktx.yaml',
+    config,
+    coreConfig: {} as KtxLocalProject['coreConfig'],
+    git: {} as KtxLocalProject['git'],
+    fileStore: {} as KtxLocalProject['fileStore'],
+  };
+}
+
+function withEmbeddings(
+  config: KtxProjectConfig,
+  embeddings: KtxProjectConfig['ingest']['embeddings'],
+): KtxProjectConfig {
+  return {
+    ...config,
+    ingest: { ...config.ingest, embeddings },
+    scan: { ...config.scan, enrichment: { ...config.scan.enrichment, embeddings } },
+  };
+}
+
+function withClaudeCodeLlm(config: KtxProjectConfig): KtxProjectConfig {
+  return {
+    ...config,
+    llm: {
+      ...config.llm,
+      provider: { backend: 'claude-code' },
+      models: { ...config.llm.models, default: 'sonnet' },
+    },
+  };
+}
+
+function baseProjectConfig(): KtxProjectConfig {
+  return withClaudeCodeLlm(buildDefaultKtxProjectConfig());
+}
+
+const stubClaudeCodeAuthProbe = async () => ({ ok: true as const });
+
+describe('buildProjectStatus embeddings', () => {
+  it('reports sentence-transformers with explicit base_url as ok', async () => {
+    const project = projectWithConfig(
+      withEmbeddings(baseProjectConfig(), {
+        backend: 'sentence-transformers',
+        model: 'all-MiniLM-L6-v2',
+        dimensions: 384,
+        sentenceTransformers: { base_url: 'http://my-st:8080', pathPrefix: '' },
+      }),
+    );
+
+    const status = await buildProjectStatus(project, {
+      claudeCodeAuthProbe: stubClaudeCodeAuthProbe,
+    });
+
+    expect(status.embeddings).toMatchObject({
+      backend: 'sentence-transformers',
+      status: 'ok',
+      detail: 'service: http://my-st:8080',
+    });
+  });
+
+  it('reports sentence-transformers with omitted base_url as managed daemon (ok)', async () => {
+    const project = projectWithConfig(
+      withEmbeddings(baseProjectConfig(), {
+        backend: 'sentence-transformers',
+        model: 'all-MiniLM-L6-v2',
+        dimensions: 384,
+      }),
+    );
+
+    const status = await buildProjectStatus(project, {
+      claudeCodeAuthProbe: stubClaudeCodeAuthProbe,
+    });
+
+    expect(status.embeddings).toMatchObject({
+      backend: 'sentence-transformers',
+      status: 'ok',
+      detail: 'managed local embeddings daemon',
+    });
+    expect(status.verdictReason).not.toMatch(/embedding credentials missing/);
+  });
+
+  it('reports sentence-transformers with empty base_url string as managed daemon (ok)', async () => {
+    const project = projectWithConfig(
+      withEmbeddings(baseProjectConfig(), {
+        backend: 'sentence-transformers',
+        model: 'all-MiniLM-L6-v2',
+        dimensions: 384,
+        sentenceTransformers: { base_url: '', pathPrefix: '' },
+      }),
+    );
+
+    const status = await buildProjectStatus(project, {
+      claudeCodeAuthProbe: stubClaudeCodeAuthProbe,
+    });
+
+    expect(status.embeddings).toMatchObject({
+      backend: 'sentence-transformers',
+      status: 'ok',
+      detail: 'managed local embeddings daemon',
+    });
+  });
+
+  it('reports openai backend with missing key as warn', async () => {
+    const project = projectWithConfig(
+      withEmbeddings(baseProjectConfig(), {
+        backend: 'openai',
+        model: 'text-embedding-3-small',
+        dimensions: 1536,
+        openai: { api_key: 'env:OPENAI_API_KEY' }, // pragma: allowlist secret
+      }),
+    );
+
+    const status = await buildProjectStatus(project, {
+      env: {},
+      claudeCodeAuthProbe: stubClaudeCodeAuthProbe,
+    });
+
+    expect(status.embeddings.status).toBe('warn');
+    expect(status.verdictReason).toMatch(/embedding credentials missing/);
+  });
+});

packages/cli/src/status-project.ts

@@ -267,9 +267,8 @@ function buildEmbeddingsStatus(config: KtxProjectEmbeddingConfig, env: NodeJS.Pr
       backend,
       model,
       dimensions,
-      status: 'warn',
-      detail: 'no base_url configured',
-      fix: 'Rerun `ktx setup`',
+      status: 'ok',
+      detail: 'managed local embeddings daemon',
     };
   }
   return { backend, model, dimensions, status: 'warn', detail: 'unknown embedding backend' };