Add frontend performance metrics pipeline to Prometheus

Collect browser-side worker round-trips, computation times, main-thread
operations, and feature counts, batch them client-side, and expose as
Prometheus histograms via a new POST /api/perf endpoint.

api/perf_routes.py

@@ -0,0 +1,43 @@
+"""Frontend performance metrics ingestion endpoint."""
+from __future__ import annotations
+
+from fastapi import APIRouter
+from pydantic import BaseModel, Field, field_validator
+
+import api.metrics as app_metrics
+
+ALLOWED_METRICS = {"worker_roundtrip", "worker_compute", "main_thread", "feature_count"}
+MAX_BATCH_SIZE = 100
+
+
+class PerfSample(BaseModel):
+    metric: str
+    operation: str = Field(max_length=50)
+    value: float = Field(ge=0, le=3600)
+
+    @field_validator("metric")
+    @classmethod
+    def validate_metric(cls, v: str) -> str:
+        if v not in ALLOWED_METRICS:
+            raise ValueError(f"Unknown metric: {v}")
+        return v
+
+
+perf_router = APIRouter(tags=["perf"])
+
+
+@perf_router.post("/api/perf", status_code=204)
+async def record_perf(samples: list[PerfSample]) -> None:
+    if len(samples) > MAX_BATCH_SIZE:
+        samples = samples[:MAX_BATCH_SIZE]
+
+    for s in samples:
+        attrs = {"operation": s.operation}
+        if s.metric == "worker_roundtrip":
+            app_metrics.frontend_worker_roundtrip.record(s.value, attrs)
+        elif s.metric == "worker_compute":
+            app_metrics.frontend_worker_compute.record(s.value, attrs)
+        elif s.metric == "main_thread":
+            app_metrics.frontend_main_thread.record(s.value, attrs)
+        elif s.metric == "feature_count":
+            app_metrics.frontend_feature_count.record(s.value)