`GET /api/v1/:slug/repositories` (filter by `format` and `kind`, keyset pagination, sort) and `GET /api/v1/:slug/repositories/:repository_name` (polymorphic `settings`). Returns counters as stored (the buffered-counter mechanism is S18/S22). Only hosted rows exist in Phase 1; the `kind` filter is defined now and returns remote and virtual repositories once S13 lands. Unblocks the frontend repository read epic (&22321). Follows the merged Phase 1 plan.