fix: honest costs in streams, oracle-sized timeouts, history & log cleanup

Cost showed $0 for every streamed request: the X-Cortiq-Cost-USD header is
written before generation, when the cost cannot be known. The gateway now
ships the final number in a closing SSE event (`cortiq_cost_usd`, alongside
the token estimate when the provider sent no usage), and the console prefers
it over the header. Money renders with 4 decimals, the last two in a smaller
font — $0.0006 stays readable instead of collapsing to $0.

Timeouts, both ends: the router default was 800 ms, silently degrading every
prompt the hosted router escalates to its oracle (~10 s) — now 15 s. Provider
clients had NO timeout at all (a dead OpenRouter host hung requests forever) —
now a 10 s connect timeout, with no overall cap so long generations and
streams are never cut.

Benchmark history: per-run × and a Clear-all button. Logs view: a clear
button backed by DELETE /admin/api/logs.

web/js/views/logs.js

@@ -21,6 +21,17 @@ export function renderLogs() {
   );
   const pauseBtn = h("button", { class: "btn ghost sm" }, "⏸ " + t("logs.pause"));
   const copyBtn = h("button", { class: "btn ghost sm" }, "⧉ " + t("common.copy"));
+  const clearBtn = h("button", { class: "btn ghost sm danger" }, "🗑 " + t("dash.clear"));
+  clearBtn.addEventListener("click", async () => {
+    try {
+      await api.clearLogs();
+      lines = [];
+      paint();
+      toast(t("dash.cleared"), "ok");
+    } catch (e) {
+      toast(String(e.message || e), "err");
+    }
+  });
 
   let lines = [];
   function paint() {
@@ -76,7 +87,7 @@ export function renderLogs() {
     h(
       "div",
       { class: "card" },
-      h("div", { class: "flex", style: "gap:8px; flex-wrap:wrap; margin-bottom:10px" }, filterIn, levelSel, pauseBtn, copyBtn),
+      h("div", { class: "flex", style: "gap:8px; flex-wrap:wrap; margin-bottom:10px" }, filterIn, levelSel, pauseBtn, copyBtn, clearBtn),
       pre
     )
   );