Make the CLI point users at the real install source

The next repo-local backlog item was ROADMAP #70: users could
mistake third-party pages or the deprecated `cargo install
claw-code` path for the official install route. The CLI now
surfaces the source of truth directly in `claw doctor` and
`claw --help`, and the roadmap closeout records the change.

Constraint: Keep the fix inside repo-local Rust CLI surfaces instead of relying on docs alone
Rejected: Close #70 with README-only wording | the bug was user-facing CLI ambiguity, so the warning needed to appear in runtime help/doctor output
Confidence: high
Scope-risk: narrow
Reversibility: clean
Directive: If install guidance changes later, update both the doctor check payload and the help-text warning together
Tested: cargo fmt --all --check; cargo clippy --workspace --all-targets -- -D warnings; cargo test --workspace; architect review APPROVE
Not-tested: Third-party websites outside this repo that may still present stale install instructions

rust/crates/rusty-claude-cli/tests/output_format_contract.rs

@@ -209,7 +209,7 @@ fn doctor_and_resume_status_emit_json_when_requested() {
     assert!(summary["failures"].as_u64().is_some());
 
     let checks = doctor["checks"].as_array().expect("doctor checks");
-    assert_eq!(checks.len(), 5);
+    assert_eq!(checks.len(), 6);
     let check_names = checks
         .iter()
         .map(|check| {
@@ -221,7 +221,27 @@ fn doctor_and_resume_status_emit_json_when_requested() {
         .collect::<Vec<_>>();
     assert_eq!(
         check_names,
-        vec!["auth", "config", "workspace", "sandbox", "system"]
+        vec![
+            "auth",
+            "config",
+            "install source",
+            "workspace",
+            "sandbox",
+            "system"
+        ]
+    );
+
+    let install_source = checks
+        .iter()
+        .find(|check| check["name"] == "install source")
+        .expect("install source check");
+    assert_eq!(
+        install_source["official_repo"],
+        "https://github.com/ultraworkers/claw-code"
+    );
+    assert_eq!(
+        install_source["deprecated_install"],
+        "cargo install claw-code"
     );
 
     let workspace = checks