test(cli): integration tests for --trace + schema breakdowns (fb-37)

Also fixes App::search_with_opts trace branch to use NoopRetriever
for SearchMode::Lexical, removing the embeddings requirement when
the user only wants lexical-mode trace.

crates/kebab-cli/tests/wire_schema_breakdowns.rs

@@ -0,0 +1,57 @@
+//! p9-fb-37: integration tests for `kebab schema --json` extended stats.
+
+mod common;
+
+use serde_json::Value;
+use std::fs;
+use std::process::Command;
+
+fn run_schema(cfg: &std::path::Path) -> Value {
+    let bin = env!("CARGO_BIN_EXE_kebab");
+    let out = Command::new(bin)
+        .args(["--config", cfg.to_str().unwrap(), "schema", "--json"])
+        .output()
+        .expect("run kebab schema");
+    assert!(
+        out.status.success(),
+        "schema failed: stderr={}",
+        String::from_utf8_lossy(&out.stderr)
+    );
+    serde_json::from_slice(&out.stdout).expect("valid JSON")
+}
+
+#[test]
+fn schema_stats_includes_breakdowns_on_fresh_corpus() {
+    let dir = tempfile::tempdir().unwrap();
+    let (cfg, workspace, _data) = common::write_config(dir.path(), 0);
+    // Run a no-op ingest to bring up migrations + create the SQLite file.
+    fs::write(workspace.join("placeholder.md"), "# placeholder\n").unwrap();
+    common::ingest(&cfg, &workspace);
+
+    let v = run_schema(&cfg);
+    let stats = &v["stats"];
+    let m = stats["media_breakdown"].as_object().unwrap();
+    assert_eq!(m.len(), 5, "5 media keys padded");
+    for k in &["markdown", "pdf", "image", "audio", "other"] {
+        assert!(m[*k].is_number(), "media[{k}] is integer");
+    }
+    assert!(stats["lang_breakdown"].is_object());
+    assert!(stats["index_bytes"]["sqlite"].is_number());
+    assert!(stats["index_bytes"]["lancedb"].is_number());
+    assert!(stats["stale_doc_count"].is_number());
+}
+
+#[test]
+fn schema_stats_breakdowns_after_ingest() {
+    let dir = tempfile::tempdir().unwrap();
+    let (cfg, workspace, _data) = common::write_config(dir.path(), 0);
+    fs::write(workspace.join("a.md"), "---\nlang: en\n---\nhello\n").unwrap();
+    fs::write(workspace.join("b.md"), "---\nlang: ko\n---\n안녕\n").unwrap();
+    common::ingest(&cfg, &workspace);
+
+    let v = run_schema(&cfg);
+    let stats = &v["stats"];
+    assert_eq!(stats["media_breakdown"]["markdown"], 2);
+    assert!(stats["lang_breakdown"].is_object());
+    assert!(stats["index_bytes"]["sqlite"].as_u64().unwrap() > 0);
+}