Cache the category tree walk (fixes ~1s File Management page load)

_build_category_index() was the one tree-scanning function never
wrapped in the app's existing 5-minute cache - it ran fresh on every
File Management page load and Sort Unsorted scan (not a manual "this
may take a moment" action like Duplicate Courses or Storage Usage), so
the cost was invisible until it was already slow. Measured ~1.0-1.1s
consistently against the live NAS-mounted library at 161 courses,
confirmed via profiling that a single call makes dozens of iterdir()
round-trips - each one a network hop over SMB. Now shares the same
cache_get_or_compute pattern and invalidate_cache() call sites as
get_all_course_dirs(), so no new invalidation logic was needed.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

README.md

@@ -137,8 +137,12 @@ silently stay blank instead of erroring.
   ones that recur across many categories (a prolific creator's name, etc.)
   so they can't outvote a genuinely specific word just by sharing more of
   them.
-  - *Refresh Library*: manually bypasses the 5-minute filesystem-scan cache,
-  for when files were added/removed directly on disk.
+  - *Refresh Library*: manually bypasses the 5-minute filesystem-scan cache
+  (this now includes the category tree Sort Unsorted/Manage Library's
+  picker builds - previously rebuilt on every page load, a full,
+  uncached walk of the whole library that got noticeably slow over a
+  NAS-mounted (SMB) library as the course count grew), for when files
+  were added/removed directly on disk.
   - *Bulk Rename*: find & replace across every course/folder name in the
   library at once, with a per-match preview and the ability to drop
   individual matches before applying. Three match modes: plain text