fix(storage,api): usage cost as per-turn delta of the sdk running total, backfill

src/beaver_gateway/frontends/api/frontend.py

@@ -6,9 +6,10 @@ write goes through ``core/conversations``; the frontend only shapes JSON.
 bus as SSE with the same keepalive the markdown frontend uses, so a proxy
 never sees a silent socket.
 
-Usage figures come from the ``usage`` table (one row per turn, API-price
-``cost_usd`` and per-model ``model_usage`` from the SDK's
-``ResultMessage``); subscription quotas come from ``rate_limits``
+Usage figures come from the ``usage`` table (one row per turn; API-price
+``cost_usd`` and per-model ``model_usage`` are per-turn deltas of the SDK's
+cumulative ``ResultMessage`` counters, see ``storage.append_usage``);
+subscription quotas come from ``rate_limits``
 (``RateLimitEvent``). The quota covers the whole subscription, so
 ``/api/limits`` puts the gateway's own spend for the window next to it
 for calibration by eye.