test: run v1.5-ported integration tests under node-env vitest project (#1307) (#1312)

* feat(test): run v1.5-ported integration tests under node-env vitest (#1307)

Adds an `integration` vitest project alongside `unit` and `storybook` so
the 13 v1.5-ported tests that need real HTTP/stdio servers (or fail under
happy-dom's SDK mock resolution) run again under node env with 30s
timeouts. Restores test-servers/ as a buildable package so the stdio
subprocess spawns a real .js file. Drops the v1.5-source `coverage.exclude`
globs and fills coverage gaps across the v1.5-ported core/ modules; two
large files (inspectorClient.ts, remote/node/server.ts) keep narrow
per-file excludes tracked in #1310.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

* test(core): address PR #1312 review — TS6-safe tsconfig, real transport_error path

- Drop `baseUrl` / `paths` / `typeRoots` / `declaration*` from
  test-servers/tsconfig.json. They were only needed for type
  resolution, and we already pass `--noCheck` from `test-servers:build`.
  Under TS 6+ the deprecated `baseUrl` exited with code 2, which
  silently skipped vitest in the `&&` chains of test:integration /
  test:coverage / validate.
- Rework the "send() throws after closed" test to drive `closed` via
  an actual transport_error SSE event instead of mutating private
  state through a cast — matches the real path the branch guards.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

---------

Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

clients/web/package.json

@@ -15,9 +15,12 @@
     "build-storybook": "storybook build",
     "test": "vitest run --project=unit",
     "test:watch": "vitest --project=unit",
-    "test:coverage": "vitest run --project=unit --coverage",
+    "test:coverage": "npm run test-servers:build && vitest run --project=unit --project=integration --coverage",
     "test:storybook": "vitest run --project=storybook",
-    "test:storybook:watch": "vitest --project=storybook"
+    "test:storybook:watch": "vitest --project=storybook",
+    "test-servers:build": "tsc -p ../../test-servers --noCheck",
+    "test:integration": "npm run test-servers:build && vitest run --project=integration",
+    "test:integration:watch": "npm run test-servers:build && vitest --project=integration"
   },
   "dependencies": {
     "@emotion/react": "^11.14.0",