feat(backend): bootstrap Go module, config, and data plane

Introduce configuration validation, Postgres migrations, Redis/storage adapters, and the seed sample video.

backend/internal/db/migrations/0014_registration_invites.sql

@@ -0,0 +1,19 @@
+-- Capacity-limited registration invite / membership links
+
+CREATE TABLE IF NOT EXISTS registration_invites (
+    id          BIGSERIAL PRIMARY KEY,
+    token_hash  TEXT NOT NULL UNIQUE,
+    token_enc   TEXT NOT NULL,
+    label       TEXT NOT NULL DEFAULT '',
+    max_uses    INT NOT NULL CHECK (max_uses > 0),
+    used_count  INT NOT NULL DEFAULT 0 CHECK (used_count >= 0),
+    status      TEXT NOT NULL DEFAULT 'active'
+                CHECK (status IN ('active', 'revoked', 'exhausted')),
+    expires_at  TIMESTAMPTZ,
+    created_by  BIGINT REFERENCES users(id) ON DELETE SET NULL,
+    created_at  TIMESTAMPTZ NOT NULL DEFAULT now(),
+    CONSTRAINT registration_invites_used_lte_max CHECK (used_count <= max_uses)
+);
+
+CREATE INDEX IF NOT EXISTS registration_invites_status_idx
+    ON registration_invites (status, created_at DESC);