feat(api): categories, tags, and storefront item filters (#23)

Adds a self-referencing categories tree, a tag registry with
deterministic colours, and item_tags, plus admin CRUD for both.

GET /api/items now accepts category, tags, min_price and max_price.
Category matching walks the subtree with a recursive CTE so selecting a
parent includes everything filed beneath it; tags match with AND via a
count check, since ANY() alone would return items carrying only one of
them. Malformed filter params return 400 rather than being ignored, so a
broken link doesn't quietly list the whole catalogue.

GET /api/filters serves the drawer its tree, tags, and price bounds in
one request.

Item image/tag aggregation moves from LEFT JOIN + GROUP BY to scalar
subqueries. Joining two one-to-many relations multiplies their rows, so
an item with 2 images and 3 tags would have repeated every image three
times once tags were added.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

backend/migrations/1786974336000_add-categories-and-tags.js

@@ -0,0 +1,60 @@
+exports.up = (pgm) => {
+  pgm.sql(`
+    CREATE TABLE IF NOT EXISTS categories (
+      id SERIAL PRIMARY KEY,
+      name TEXT NOT NULL,
+      parent_id INTEGER REFERENCES categories(id) ON DELETE CASCADE,
+      sort_order INTEGER NOT NULL DEFAULT 0,
+      created_at TIMESTAMPTZ NOT NULL DEFAULT now()
+    );
+
+    -- Siblings can't share a name. Two partial indexes rather than one plain
+    -- unique constraint, because a NULL parent_id (a root category) compares
+    -- unequal to every other NULL and would let duplicate roots straight in.
+    CREATE UNIQUE INDEX IF NOT EXISTS categories_child_name_uniq
+      ON categories (parent_id, lower(name)) WHERE parent_id IS NOT NULL;
+    CREATE UNIQUE INDEX IF NOT EXISTS categories_root_name_uniq
+      ON categories (lower(name)) WHERE parent_id IS NULL;
+
+    CREATE INDEX IF NOT EXISTS categories_parent_id_idx ON categories (parent_id);
+
+    CREATE TABLE IF NOT EXISTS tags (
+      id SERIAL PRIMARY KEY,
+      name TEXT NOT NULL,
+      color TEXT NOT NULL,
+      created_at TIMESTAMPTZ NOT NULL DEFAULT now()
+    );
+
+    CREATE UNIQUE INDEX IF NOT EXISTS tags_name_uniq ON tags (lower(name));
+
+    CREATE TABLE IF NOT EXISTS item_tags (
+      item_id INTEGER NOT NULL REFERENCES items(id) ON DELETE CASCADE,
+      tag_id INTEGER NOT NULL REFERENCES tags(id) ON DELETE CASCADE,
+      PRIMARY KEY (item_id, tag_id)
+    );
+
+    -- The item_id half is covered by the primary key; filtering by tag needs
+    -- the other direction.
+    CREATE INDEX IF NOT EXISTS item_tags_tag_id_idx ON item_tags (tag_id);
+
+    -- Deleting a category leaves its items in place and merely uncategorized,
+    -- rather than taking inventory down with it.
+    ALTER TABLE items ADD COLUMN IF NOT EXISTS category_id INTEGER
+      REFERENCES categories(id) ON DELETE SET NULL;
+
+    CREATE INDEX IF NOT EXISTS items_category_id_idx ON items (category_id);
+  `);
+};
+
+// Unlike the baseline migration, this one is safe to reverse: it drops only
+// what it created. Item rows themselves are untouched — they just lose their
+// category assignment along with the column.
+exports.down = (pgm) => {
+  pgm.sql(`
+    DROP INDEX IF EXISTS items_category_id_idx;
+    ALTER TABLE items DROP COLUMN IF EXISTS category_id;
+    DROP TABLE IF EXISTS item_tags;
+    DROP TABLE IF EXISTS tags;
+    DROP TABLE IF EXISTS categories;
+  `);
+};