FE-1222, FE-1226: Classify optimization transport errors, auto-reconnect runs by id + cursor, and remove the legacy optimization path

.changeset/eight-streams-return.md

@@ -0,0 +1,6 @@
+---
+"@hashintel/petrinaut-core": patch
+"@hashintel/petrinaut": patch
+---
+
+Make optimization runs detached and resumable — and make that the only contract. Optimization events carry a server-issued `seq`; the host optimization capability is now `createOptimizationRun`/`attachOptimizationRun`/`cancelOptimizationRun` (all required; attachments accept an `onAttached` callback so UIs can report an honest connection state), and the legacy single-connection `optimize` method is removed. The optimizations UI auto-reconnects dropped event streams by run id and cursor, re-attaching after page reloads where storage allows.

.changeset/fe-1225-optimization-event-seq.md

@@ -0,0 +1,5 @@
+---
+"@hashintel/petrinaut-core": patch
+---
+
+Add an optional `seq` sequence number to every optimization event so detached, reconnectable optimization runs can be resumed from a cursor.

apps/hash-api/README.md

@@ -37,6 +37,15 @@ The HASH Backend API service is configured using the following environment varia
     together to enable Petrinaut optimization. The authenticated capabilities
     endpoint reports this configuration independently of service health, so a
     temporary optimizer outage does not make the feature disappear from HASH.
+  - NodeAPI proxies detached, reconnectable optimization runs:
+    `POST /api/petrinaut-optimizer/optimize/runs` starts a run and returns its
+    id, `GET /api/petrinaut-optimizer/optimize/runs/:runId/events?cursor=N`
+    attaches to (and resumes) its NDJSON event stream without affecting the
+    run, and `DELETE /api/petrinaut-optimizer/optimize/runs/:runId` cancels
+    it. NodeAPI is a thin proxy: it authenticates, rate-limits, and
+    validates, then forwards with the account's `x-hash-account-id` tag —
+    the optimizer itself enforces per-account single-flight and owner-only
+    run visibility.
 - `FRONTEND_URL`: The URL the frontend is hosted on.
 - Vault
   - `HASH_VAULT_HOST`: The host address (including protocol) that the Vault server is running on, e.g. `http://127.0.0.1`