Decide whether after-response provider lookups run after a Trusted-Server-generated 502 #1561

Follow-up from PR #1487 (review round 3).

Description

When the publisher origin is unreachable, Trusted Server generates a 502 itself. After-response provider lookups still run for that request. This is documented behaviour in #1487, but none of the follow-ups #1547–#1556 tracks revisiting it.

Open question: should a request that ends in a Trusted-Server-generated 502 dispatch vendor lookups (sending the EC ID, IP and UA to providers) when the page never rendered? Options include skipping lookups on TS-generated 5xx, skipping them on any non-2xx page response, or keeping current behaviour with the rationale written down.

Done when

• A decision is recorded on whether after-response lookups run after a TS-generated 502 (origin unreachable).
• If behaviour changes, the gate is implemented and pinned by a test on each adapter that runs after-response lookups.
• Docs describe the chosen behaviour.

Affected area

Core (Edge Cookies, GDPR)

Code: crates/trusted-server-core/src/ec/after_response.rs.