perf(usage): bound lastUsed overlay scan to 2-day window; reach max thinking tier

getUsageStats("all") shipped the entire usageHistory table to JS just to
refine lastUsed (~2s on 290K rows, on every statsEmitter update per SSE
listener). Bound the overlay to a 2-day indexed range scan; older entries
keep day-level lastUsed from usageDaily aggregates. Totals unaffected.

budgetToLevel now maps budgets > 80384 (midpoint of 32768/128000) to
"max" instead of clamping to "xhigh", so the top reasoning tier is
reachable from large budget_tokens requests.

tests/unit/thinking-budget-max-level.test.js

@@ -0,0 +1,39 @@
+import { describe, expect, it } from "vitest";
+import { budgetToLevel } from "../../open-sse/translator/concerns/thinking.js";
+import { applyThinking } from "../../open-sse/translator/concerns/thinkingUnified.js";
+import { FORMATS } from "../../open-sse/translator/formats.js";
+
+// Reverse map must be able to reach "max": LEVEL_TO_BUDGET.max = 128000 and
+// xhigh = 32768, so the xhigh/max threshold is their midpoint (80384).
+// Previously any budget > 28672 collapsed to "xhigh", making "max"
+// unreachable from Claude Code budget_tokens — its default thinking budget
+// (MAX_THINKING_TOKENS) could never produce effort "max".
+describe("budgetToLevel reaches max tier", () => {
+  it("budget 98304 → \"max\"", () => {
+    expect(budgetToLevel(98304)).toBe("max");
+  });
+
+  it("budget 128000 → \"max\"", () => {
+    expect(budgetToLevel(128000)).toBe("max");
+  });
+
+  it("budget 80385 → \"max\" (just above midpoint)", () => {
+    expect(budgetToLevel(80385)).toBe("max");
+  });
+
+  it("budget 80384 → \"xhigh\" (midpoint still xhigh)", () => {
+    expect(budgetToLevel(80384)).toBe("xhigh");
+  });
+
+  it("budget 31999 stays \"xhigh\"", () => {
+    expect(budgetToLevel(31999)).toBe("xhigh");
+  });
+});
+
+describe("applyThinking (openai-responses): large budgets map to max effort", () => {
+  it("budget 98304 → reasoning_effort \"max\" for gpt-5.6-sol (openai wire)", () => {
+    const body = { thinking: { type: "enabled", budget_tokens: 98304 } };
+    const out = applyThinking(FORMATS.OPENAI_RESPONSES, "gpt-5.6-sol", body, "codex");
+    expect(out?.reasoning_effort).toBe("max");
+  });
+});