fix(api): clear the six API-route TypeScript regressions the new gate landed red on

#11705 froze config/quality/api-typecheck-baseline.json days before it merged;
by then six diagnostics had regressed on release/v3.8.51, so the gate turned
every open PR red on arrival (api-route-typecheck run 33299099596):

- webhooks/[id]/test/route.ts: duplicate `import { getWebhook, recordWebhookDelivery }`
  left by the barrel migration (#12051) — a real defect, ESM rejects duplicate
  bindings at load time.
- providers/volcengine-plan/connect/**: `if (!x.ok)` / `if (!validation.success)`
  do not narrow discriminated unions without strictNullChecks (repo is
  strict:false) — compare `=== false` so `.error` type-checks.
- providers/route.ts: type the ["id","provider"] column projection instead of
  passing `unknown` into cleanupProviderModelsAfterConnectionDelete.
- tunnels/tailscale/install/route.ts: spread PublicSafeTunnelErrorBody into the
  Record<string, unknown> payload pushEvent expects.

Gate back to OK (289 errors, all frozen) and the 12 diagnostics that had
disappeared since the freeze are ratcheted out of the baseline (--update).

config/quality/api-typecheck-baseline.json

@@ -158,7 +158,7 @@
   "src/app/api/providers/route.ts": {
     "TS2352": 1,
     "TS2322": 2,
-    "TS2345": 4
+    "TS2345": 3
   },
   "src/app/api/providers/test-batch/route.ts": {
     "TS2345": 4
@@ -182,8 +182,7 @@
     "TS2739": 1
   },
   "src/app/api/providers/volcengine-plan/connect/route.ts": {
-    "TS2739": 1,
-    "TS2339": 1
+    "TS2739": 1
   },
   "src/app/api/radar/local-model-state/route.ts": {
     "TS2339": 4
@@ -256,15 +255,6 @@
     "TS2345": 1,
     "TS2322": 1
   },
-  "src/app/api/tunnels/cloudflared/route.ts": {
-    "TS2339": 1
-  },
-  "src/app/api/tunnels/ngrok/route.ts": {
-    "TS2339": 1
-  },
-  "src/app/api/tunnels/tailscale/routeUtils.ts": {
-    "TS2339": 1
-  },
   "src/app/api/usage/analytics/route.ts": {
     "TS2352": 15
   },
@@ -274,9 +264,6 @@
   "src/app/api/v1/batches/route.ts": {
     "TS2339": 1
   },
-  "src/app/api/v1/chatgpt-web/image/[id]/route.ts": {
-    "TS2345": 1
-  },
   "src/app/api/v1/classify/route.ts": {
     "TS2322": 1
   },
@@ -287,8 +274,8 @@
     "TS2339": 1
   },
   "src/app/api/v1/images/edits/route.ts": {
-    "TS2339": 21,
-    "TS2322": 5
+    "TS2339": 18,
+    "TS2322": 4
   },
   "src/app/api/v1/messages/count_tokens/route.ts": {
     "TS2339": 2,
@@ -356,12 +343,6 @@
   "src/lib/db/tierConfig.ts": {
     "TS2345": 2
   },
-  "src/lib/guardrails/videoBridgeHelpers.ts": {
-    "TS2488": 1,
-    "TS2365": 2,
-    "TS2322": 1,
-    "TS2345": 1
-  },
   "src/lib/monitoring/comboHealthAutopilot.ts": {
     "TS2305": 1,
     "TS2345": 1