Measure Axum's per-request HTTP client against a pooled one #1585

Summary

Measure Axum's per-request HTTP client against a pooled one, and keep it per request unless the measurement shows the Next.js regression gone (SH-1's exception).

Part of #1558, server-side identity on every adapter. Plan ID T4, planned in wave 2 (MVP: Fastly and Axum); priority P2, size S. Design: spec; order and dependencies: plan.

Requirements

SH-1 Built once

Settings, the partner registry, store clients and the HTTP client are built once per process or isolate.

Current state

What the code does today, from the design's survey at the revisions it names:

• SH-1: Cloudflare and Spin rebuild app state per request; Axum builds the partner registry per request (app.rs:495 at Cut Trusted Server over to EdgeZero PR 275 #1506's head 9ec4711d3) and the HTTP client per request on purpose, because a pooled client regressed a Next.js flow (main platform.rs:620-623). Keep that client choice unless a measurement shows the regression gone.

Acceptance criteria

• SH-1: An adapter test shows settings, the partner registry and store clients built once across two requests, and the HTTP client too, except Axum's, which stays per request until a measurement shows the Next.js regression gone
• SH-1: After that measurement Axum's client is held to the same rule

Dependencies

Blocked by:

• Cut Trusted Server over to EdgeZero PR 275 #1507 Cut Trusted Server over to EdgeZero PR 275

Notes from the plan

• Cut Trusted Server over to EdgeZero PR 275 #1507 delivers the cutover and stays under Integrate Auctioneer into Trusted Server on EdgeZero PR 275 #1505; it blocks A1, T4, T5, T21, Reduce Fastly adapter per-request fixed cost: defer KV/geo work, cache settings/registry/template fingerprint #1192 and Certificate checks on identity backends that still follow proxy.certificate_check #1556.