feat(plex): collections — sync, browse, filter, and info-page strips (Phase 1, read)

Backend (migration 0047_plex_collections): a plex_collections table mirrors every Plex
collection (card metadata + smart flag + an editable flag reserved for Phase 2); membership
is stored as GIN-indexed collection_keys on member movies (plex_items) and shows (plex_shows).
The background sync (plex_sync) now fetches each library's collections + their children and
rebuilds membership — so ALL reads are local (Plex's dual-language collection queries are slow;
this trades a ~4-min background sync for instant reads). New /api/plex/collections endpoint;
/browse gains a combinable  filter; item_detail returns the movie's collection
'strips' (sibling titles as playable cards, smallest/most-specific collection first) — all pure
local lookups.

Frontend: PlexSidebar gains a searchable Collection picker + an active-collection chip;
PlexInfo renders the collection strips (playable posters + 'Browse collection' → sets the
filter); the collection is part of PlexFilters (persisted). i18n en/hu/de.

Phase 2 (create/edit collections with write-back to Plex) is separate.

backend/alembic/versions/0047_plex_collections.py

@@ -0,0 +1,57 @@
+"""Plex collections
+
+Revision ID: 0047_plex_collections
+Revises: 0046_plex_people_search
+Create Date: 2026-07-06
+
+Mirrors Plex collections locally so reads never hit Plex's slow (dual-language) collection queries.
+A `plex_collections` table holds each collection's card metadata; membership is stored as GIN-indexed
+`collection_keys` on the member movies (plex_items) and shows (plex_shows), so a collection can be a
+combinable filter and a title's "collection strip" is a pure local lookup. `editable` marks the
+(curated) collections we may later write back to Plex; everything is read-only by default.
+"""
+from typing import Sequence, Union
+
+import sqlalchemy as sa
+from alembic import op
+from sqlalchemy.dialects import postgresql
+
+revision: str = "0047_plex_collections"
+down_revision: Union[str, None] = "0046_plex_people_search"
+branch_labels: Union[str, Sequence[str], None] = None
+depends_on: Union[str, Sequence[str], None] = None
+
+
+def upgrade() -> None:
+    op.create_table(
+        "plex_collections",
+        sa.Column("id", sa.Integer(), primary_key=True),
+        sa.Column("rating_key", sa.String(length=32), nullable=False),
+        sa.Column("library_id", sa.Integer(), sa.ForeignKey("plex_libraries.id", ondelete="CASCADE"), nullable=False),
+        sa.Column("title", sa.String(length=512), nullable=False),
+        sa.Column("summary", sa.Text(), nullable=True),
+        sa.Column("thumb_key", sa.String(length=512), nullable=True),
+        sa.Column("child_count", sa.Integer(), nullable=True),
+        sa.Column("smart", sa.Boolean(), nullable=False, server_default="false"),
+        sa.Column("editable", sa.Boolean(), nullable=False, server_default="false"),
+        sa.Column("synced_at", sa.DateTime(timezone=True), nullable=True),
+        sa.Column("created_at", sa.DateTime(timezone=True), server_default=sa.text("now()"), nullable=False),
+        sa.Column("updated_at", sa.DateTime(timezone=True), server_default=sa.text("now()"), nullable=False),
+    )
+    op.create_index("ix_plex_collections_rating_key", "plex_collections", ["rating_key"], unique=True)
+    op.create_index("ix_plex_collections_library_id", "plex_collections", ["library_id"])
+
+    op.add_column("plex_items", sa.Column("collection_keys", postgresql.JSONB(), nullable=True))
+    op.create_index("ix_plex_items_collections_gin", "plex_items", ["collection_keys"], postgresql_using="gin")
+    op.add_column("plex_shows", sa.Column("collection_keys", postgresql.JSONB(), nullable=True))
+    op.create_index("ix_plex_shows_collections_gin", "plex_shows", ["collection_keys"], postgresql_using="gin")
+
+
+def downgrade() -> None:
+    op.drop_index("ix_plex_shows_collections_gin", table_name="plex_shows")
+    op.drop_column("plex_shows", "collection_keys")
+    op.drop_index("ix_plex_items_collections_gin", table_name="plex_items")
+    op.drop_column("plex_items", "collection_keys")
+    op.drop_index("ix_plex_collections_library_id", table_name="plex_collections")
+    op.drop_index("ix_plex_collections_rating_key", table_name="plex_collections")
+    op.drop_table("plex_collections")