fix(clients): flatten scoped remote output

- Render explicit --remote clients results with profile-only labels.

- Suppress remote host group headers for scoped client queries.

- Keep global and mixed client listings grouped by host.

- Update client and CLI tests for scoped remote rendering.

- Bump browser-cli and extension versions to 0.16.5.

browser_cli/client/core.py

@@ -151,21 +151,25 @@ def active_browser_targets(*, include_remotes: bool = True, key=None, suppress_p
     targets.extend(_remote_browser_targets(key=key, suppress_pq_warning=suppress_pq_warning))
   return targets
 
-def _cached_client_row(target: BrowserTarget) -> dict | None:
+def _cached_client_row(target: BrowserTarget, *, scoped: bool = False) -> dict | None:
   """Build a clients row from a target's discovery data, skipping a roundtrip.
 
   Returns None when the remote didn't advertise its version (older serve), so
-  callers fall back to an explicit ``clients.list`` query.
+  callers fall back to an explicit ``clients.list`` query. When *scoped* is
+  true, the caller already selected one remote host, so render profile-only
+  labels instead of adding a host group header.
   """
   if target.version is None and target.extension_version is None:
     return None
-  return {
-    "profile": target.display_name,
-    "profileGroup": target.display_group,
+  row = {
+    "profile": target.profile if scoped else target.display_name,
     "name": target.browser_name or "",
     "version": target.version or "",
     "extensionVersion": target.extension_version or "",
   }
+  if target.display_group and not scoped:
+    row["profileGroup"] = target.display_group
+  return row
 
 def _rows_from_result(result, label: str, profile_group: str | None) -> list[dict]:
   rows = []
@@ -249,18 +253,17 @@ def collect_browser_clients(
     if targets:
       uncached = []
       for target in targets:
-        cached = _cached_client_row(target)
+        cached = _cached_client_row(target, scoped=True)
         if cached is not None:
           rows.append(cached)
         else:
           uncached.append(target)
       results = _run_concurrent([
         (lambda t=t: _client_rows_async(
-          t.display_name,
+          t.profile,
           profile=t.profile,
           remote=remote,
           key=key,
-          profile_group=t.display_group,
         ))
         for t in uncached
       ])