feat(backend): add standalone data plane

Replace the Supabase application data plane with the Node/PostgreSQL API, migrate mobile, admin, web, and MCP callers, add controlled cutover tooling, and define hardened Dokploy infrastructure.

apps/api/drizzle/0008_residual_realtime.sql

@@ -0,0 +1,15 @@
+ALTER TABLE profiles
+  ADD COLUMN IF NOT EXISTS last_nudge_sent_at timestamptz;
+--> statement-breakpoint
+CREATE TABLE IF NOT EXISTS live_draw_sessions (
+  couple_id uuid PRIMARY KEY REFERENCES couples(id) ON DELETE CASCADE,
+  strokes jsonb NOT NULL DEFAULT '[]'::jsonb,
+  revision bigint NOT NULL DEFAULT 1,
+  updated_by uuid NOT NULL REFERENCES profiles(id) ON DELETE CASCADE,
+  created_at timestamptz NOT NULL DEFAULT now(),
+  updated_at timestamptz NOT NULL DEFAULT now(),
+  CONSTRAINT live_draw_sessions_strokes_array CHECK (jsonb_typeof(strokes) = 'array')
+);
+--> statement-breakpoint
+CREATE INDEX IF NOT EXISTS live_draw_sessions_updated_at_idx
+  ON live_draw_sessions(updated_at DESC);