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/api.js

@@ -130,6 +130,7 @@ export const api = {
   // system / logs / lifecycle
   system: () => j("GET", "/system"),
   logs: (limit = 300) => j("GET", "/logs?limit=" + limit),
+  clearLogs: () => j("DELETE", "/logs"),
   restart: () => j("POST", "/restart"),
   benchStart: (model) => j("POST", "/bench", { model }),
   benchList: () => j("GET", "/bench"),
@@ -190,6 +191,7 @@ export async function testStream(body, onDelta) {
   let ttftMs = null; // time to first content token
   let usage = null; // OpenAI-style final-chunk usage, when the provider sends it
   let usageEstimated = false; // gateway-injected estimate rather than tokenizer truth
+  let costUsd = null; // final cost from the gateway's closing event (headers carry 0)
   for (;;) {
     const { done, value } = await reader.read();
     if (done) break;
@@ -207,6 +209,7 @@ export async function testStream(body, onDelta) {
           usage = chunk.usage;
           usageEstimated = !!chunk.cortiq_estimated;
         }
+        if (chunk.cortiq_cost_usd != null) costUsd = chunk.cortiq_cost_usd;
         const d = chunk.choices?.[0]?.delta?.content;
         if (d) {
           if (ttftMs == null) ttftMs = Math.round(performance.now() - t0);
@@ -224,7 +227,7 @@ export async function testStream(body, onDelta) {
     score: parseFloat(h.get("x-cortiq-complexity-score") || "0"),
     selected_model: h.get("x-cortiq-selected-model") || "",
     route_source: h.get("x-cortiq-route-source") || "",
-    cost_usd: parseFloat(h.get("x-cortiq-cost-usd") || "0"),
+    cost_usd: costUsd != null ? costUsd : parseFloat(h.get("x-cortiq-cost-usd") || "0"),
     usage,
     usage_estimated: usageEstimated,
     ttft_ms: ttftMs,