feat: decouple billing correctness from usage log batching

backend/migrations/071_add_usage_billing_dedup.sql

@@ -0,0 +1,13 @@
+-- 窄表账务幂等键：将“是否已扣费”从 usage_logs 解耦出来
+-- 幂等执行：可重复运行
+
+CREATE TABLE IF NOT EXISTS usage_billing_dedup (
+    id BIGSERIAL PRIMARY KEY,
+    request_id VARCHAR(255) NOT NULL,
+    api_key_id BIGINT NOT NULL,
+    request_fingerprint VARCHAR(64) NOT NULL,
+    created_at TIMESTAMPTZ NOT NULL DEFAULT NOW()
+);
+
+CREATE UNIQUE INDEX IF NOT EXISTS idx_usage_billing_dedup_request_api_key
+    ON usage_billing_dedup (request_id, api_key_id);

backend/migrations/072_add_usage_billing_dedup_created_at_brin_notx.sql

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+-- usage_billing_dedup 是按时间追加写入的幂等窄表。
+-- 使用 BRIN 支撑按 created_at 的批量保留期清理，尽量降低写放大。
+-- 使用 CONCURRENTLY 避免在热表上长时间阻塞写入。
+
+CREATE INDEX CONCURRENTLY IF NOT EXISTS idx_usage_billing_dedup_created_at_brin
+    ON usage_billing_dedup
+    USING BRIN (created_at);

backend/migrations/073_add_usage_billing_dedup_archive.sql

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+-- 冷归档旧账务幂等键，缩小热表索引与清理范围，同时不丢失长期去重能力。
+
+CREATE TABLE IF NOT EXISTS usage_billing_dedup_archive (
+    request_id VARCHAR(255) NOT NULL,
+    api_key_id BIGINT NOT NULL,
+    request_fingerprint VARCHAR(64) NOT NULL,
+    created_at TIMESTAMPTZ NOT NULL,
+    archived_at TIMESTAMPTZ NOT NULL DEFAULT NOW(),
+    PRIMARY KEY (request_id, api_key_id)
+);