feat(channels): search box + clickable tag chips; fix(feed): contextual Your-tags

- Channels manager: prominent channel-name search box and the 'Your tags' chips are now
  clickable to filter the table by tag (replacing the hidden per-column DataTable popovers).
  Both filter client-side over the status-filtered list; a focus-channel intent seeds the
  search, the reset intent clears both.
- Feed 'Your tags' sidebar: count user tags in the facet endpoint (the 'other' category) and
  make the widget contextual like language/topic — counts reflect the current filter and
  zero-count chips hide (e.g. a source=search view with no tagged channels shows 'no matching
  tags' instead of the full static list). EN/HU/DE searchPlaceholder.

backend/app/routes/feed.py

@@ -535,7 +535,7 @@ def get_facets(
     (tag ids)."""
     visible = or_(ChannelTag.user_id.is_(None), ChannelTag.user_id == user.id)
     counts: dict[int, int] = {}
-    for category in ("language", "topic"):
+    for category in ("language", "topic", "other"):
         # Disjunctive (OR) facets drop the category's own selections so its chips keep
         # independent counts (you can OR more of them in). Conjunctive (AND, topics only)
         # keeps them applied, so each remaining chip narrows to channels that ALSO have all