feat(images): store images' own categories in the library database (#332)

One new table, image_categories, and its category index, created empty
by a forward-only migration that reads and writes only its own objects.
Startup checks the structure; restore also checks the values. The store
sets, clears and reads own categories by file key (the deepest output
source holding the file and the path below it), and copies a removed
duplicate's category to a kept copy that has none.

py/api/images.py

@@ -800,6 +800,49 @@ def _favorite_root_key(root) -> str:
     return _favorite_relative_key(os.path.realpath(str(root)))
 
 
+def _source_depth(source: str) -> int:
+    return len([part for part in re.split(r"[\\/]+", source) if part])
+
+
+def deepest_source(sources, absolute_path):
+    """``(source, POSIX path below it)`` of the deepest source holding the path.
+
+    *sources* are compared by their real path (they are stored resolved); the
+    path is compared lexically after ``normpath`` and never resolved, so a
+    symlinked subfolder keeps its listed spelling. Containment folds case
+    where the OS does. None when no source contains the path.
+    """
+    path = os.path.normpath(str(absolute_path))
+    folded = os.path.normcase(path)
+    best = None
+    for source in sources:
+        real = os.path.normpath(os.path.realpath(str(source)))
+        prefix = os.path.join(os.path.normcase(real), "")
+        if not folded.startswith(prefix):
+            continue
+        if best is None or _source_depth(real) > _source_depth(best):
+            best = real
+    if best is None:
+        return None
+    relative = os.path.relpath(path, best)
+    return best, relative.replace(os.sep, "/")
+
+
+def image_category_key(sources, absolute_path):
+    """The file key of an image's own category (#332), or None.
+
+    ``(root key, relative key)``: the deepest output source that contains the
+    file and the path below it, keyed with the favorites helpers. Without
+    nested sources it equals the file's favorite key. A path no source
+    contains has no key (and so no own category).
+    """
+    found = deepest_source(sources, absolute_path)
+    if found is None:
+        return None
+    source, relative = found
+    return _favorite_root_key(source), _favorite_relative_key(relative)
+
+
 def _name_suffix(name):
     """``Path(name).suffix`` as Python 3.10-3.13 compute it.