feat(kb): drag-to-resize splitter + search survives view switch

Two requests on top of v0.1.9:

1. Drag-to-resize splitter
   The previous fixed Bootstrap col-md-5/col-md-7 split locked the
   user into 41.66% answer / 58.33% PDF. Replaced with a flex-row
   layout containing a 6px drag handle. mousedown spawns a fixed
   transparent overlay so the PDF.js iframe doesn't swallow mouse
   events while dragging; mouseup persists the chosen ratio (clamped
   15-85%) to localStorage as kb-split-pct, so the next page-load and
   the next session both come back to the same layout. Both the
   ask split view and the search split view share _buildSplitShell +
   _wireSplitter — single source of truth for the geometry.

2. Search survives a view switch
   Search had the same view-bound promise problem ask had before
   v0.1.9. Hoisted the in-flight request to a module-level
   _activeSearch and the most recent {query, kind, hits, selectedIdx}
   to _lastSearch + sessionStorage. afterRender restores the input,
   the kind filter, the hit list (with the same hit highlighted), and
   the right-pane preview. Click handler updates selectedIdx so a
   round-trip lands on the user's last-clicked hit, not always on the
   top-ranked one.

The persistence helpers grew a tiny refactor: _loadJson/_saveJson/_clear
replace the ask-only SS_KEY shim and now back both ask + search keys.

Refs Task Master #5, #6

manifest.json

@@ -1,7 +1,7 @@
 {
     "name": "KnowledgeBase",
     "module": "KnowledgeBase",
-    "version": "0.1.9",
+    "version": "0.1.10",
     "acceptableVersions": [
         ">=8.0.0"
     ],