Replace Date.now() with performance.now() for duration measurements (#258)

* Replace Date.now() with performance.now() for duration measurements

- Import performance from node:perf_hooks in all affected files
- Update Timer and ThinkingTimer classes to use performance.now()
- Update activity tracking (markActivity, getIdleMs) to use performance.now()
- Update cache duration measurements to use performance.now()
- Update agent execution timing (cursor, opencode) to use performance.now()
- Update subprocess execution timing to use performance.now()
- Update API performance monitoring to use performance.now()
- Update prep phase timing to use performance.now()
- Update timer.test.ts to mock performance.now() instead of Date.now()

Benefits:
- Monotonic clock immune to system clock adjustments
- Higher precision (microsecond vs millisecond resolution)
- Purpose-built for performance measurement

Fixes #245

* fix lint.

* Round float durations to integers in logging

Preserve original behavior by rounding performance.now() float values
to integers when displaying/logging millisecond durations.

* fix lint.

---------

Co-authored-by: pullfrog[bot] <226033991+pullfrog[bot]@users.noreply.github.com>
Co-authored-by: Robin Tail <robin_tail@me.com>

utils/timer.ts

@@ -1,3 +1,4 @@
+import { performance } from "node:perf_hooks";
 import { log } from "./cli.ts";
 
 export class Timer {
@@ -5,11 +6,11 @@ export class Timer {
   private lastCheckpointTimestamp: number | null = null;
 
   constructor() {
-    this.initialTimestamp = Date.now();
+    this.initialTimestamp = performance.now();
   }
 
   checkpoint(name: string): void {
-    const now = Date.now();
+    const now = performance.now();
     const duration = this.lastCheckpointTimestamp
       ? now - this.lastCheckpointTimestamp
       : now - this.initialTimestamp;
@@ -33,12 +34,12 @@ export class ThinkingTimer {
   private lastToolResultTimestamp: number | null = null;
 
   markToolResult(): void {
-    this.lastToolResultTimestamp = Date.now();
+    this.lastToolResultTimestamp = performance.now();
     log.debug(`» thinking timer: markToolResult at ${this.lastToolResultTimestamp}`);
   }
 
   markToolCall(): void {
-    const now = Date.now();
+    const now = performance.now();
     log.debug(
       `» thinking timer: markToolCall at ${now}, lastToolResult=${this.lastToolResultTimestamp}`
     );