feat(version): extension reports its version; doctor shows all-component coherence

The upgrade story spanned four parts (CLI, daemon, extension, skill) with no
single view and — worst — the extension was a total black box: nothing reported
which build was live, so a user could sit on a stale extension with zero signal.

- ext (0.4.7): on connect the extension sends a `hello` with
  chrome.runtime.getManifest().version; the native-messaging host records it to a
  `relay-ext-version` sidecar (next to relay-cdp-url, removed on exit).
- build.rs embeds the shipped extension version (AB_CONNECT_VERSION, read from the
  ext manifest at compile time) so the CLI knows what extension it expects.
- `chrome-use doctor` gains a Versions section: CLI (vs the cached latest from the
  background update check), extension (connected version vs the bundled expected —
  warns + tells you to reload it in Chrome if behind), and skill (bundled, version-
  locked; `skills add` copies may be stale). Daemon coherence was already covered.

So 'which of the four parts is on what version, and what needs upgrading' is now
one command. Verified: doctor warns on a simulated old extension and passes on a
current one; gracefully shows 'not connected / predates reporting' when the host
hasn't learned a version yet.

cli/src/doctor/versions.rs

@@ -0,0 +1,89 @@
+//! Version-coherence checks across all four moving parts: the CLI binary, the
+//! per-session daemons (covered by `daemon.rs`), the connected `ab-connect`
+//! extension, and the bundled skill. The extension was previously a black box —
+//! nothing reported which build was live — so a user could sit on an old
+//! extension with no signal. The extension now reports its version over the
+//! relay (`hello`), the host records it, and this surfaces it in one place.
+
+use super::{Check, Status};
+use crate::{connect, upgrade};
+
+pub(super) fn check(checks: &mut Vec<Check>) {
+    let category = "Versions";
+    let cli_version = env!("CARGO_PKG_VERSION");
+
+    // CLI — compare against the latest seen by the background update check.
+    match upgrade::cached_latest_version() {
+        Some(latest) if upgrade::version_is_newer(&latest, cli_version) => {
+            checks.push(
+                Check::new(
+                    "versions.cli",
+                    category,
+                    Status::Warn,
+                    format!("CLI {cli_version} (newer available: {latest})"),
+                )
+                .with_fix("chrome-use upgrade".to_string()),
+            );
+        }
+        _ => {
+            checks.push(Check::new(
+                "versions.cli",
+                category,
+                Status::Pass,
+                format!("CLI {cli_version}"),
+            ));
+        }
+    }
+
+    // Extension — the build this CLI shipped alongside (embedded at compile time
+    // from the extension manifest) is what we expect to be running.
+    let expected_ext = env!("AB_CONNECT_VERSION");
+    match connect::relay_ext_version() {
+        Some(ext) if upgrade::version_is_newer(expected_ext, &ext) => {
+            checks.push(
+                Check::new(
+                    "versions.extension",
+                    category,
+                    Status::Warn,
+                    format!("extension {ext} is behind the bundled {expected_ext}"),
+                )
+                .with_fix(
+                    "update ab-connect in Chrome: chrome://extensions \u{2192} reload \
+                     (or wait for the Web Store auto-update)"
+                        .to_string(),
+                ),
+            );
+        }
+        Some(ext) => {
+            checks.push(Check::new(
+                "versions.extension",
+                category,
+                Status::Pass,
+                format!("extension {ext}"),
+            ));
+        }
+        None => {
+            checks.push(Check::new(
+                "versions.extension",
+                category,
+                Status::Info,
+                format!(
+                    "extension not connected (or it predates version reporting — \
+                     expected {expected_ext})"
+                ),
+            ));
+        }
+    }
+
+    // Skill — ships inside the same release artifact as the binary, so it's
+    // version-locked here. Copies made elsewhere via `skills add` aren't.
+    checks.push(Check::new(
+        "versions.skill",
+        category,
+        Status::Info,
+        format!(
+            "skills bundled with this CLI ({cli_version}); copies made via `skills add` \
+             elsewhere may be stale — re-run to refresh"
+        ),
+    ));
+}