fix(build): stop the host tree leaking into the image, split the tsc lanes

Review round 1 fallout, all of it verified against real builds:

- .dockerignore: `node_modules/` is anchored at the context root and has no
  implicit `**/` (unlike gitignore), so it never matched frontend/node_modules.
  `COPY frontend/ ./` was overlaying the Windows host's node_modules on top of
  what `npm ci` had installed — the image carried @esbuild/win32-x64 and 31 .cmd
  shims, and the new typecheck ran a tsc resolved from that merged tree. Build
  context transfer drops 3.05 GB -> 19 kB. Also excludes e2e/.auth (a live
  Playwright session), the report/result dirs and logs.
- build no longer type-checks the e2e project: a type error in a spec must not
  make the app unbuildable for a self-hoster. The gate still checks it via
  `npm run typecheck` (now three named lanes).
- tsconfig.json references tsconfig.node.json, so editors check vite.config.ts /
  vitest.config.ts under the same config the gate uses instead of an inferred one.
- vitest include accepts .test.tsx: an uncollected test file does not fail, it
  silently never runs.

.dockerignore

@@ -6,8 +6,17 @@
 **/*.pyc
 .venv/
 venv/
-node_modules/
+# Docker patterns are anchored at the context root with NO implicit `**/` (unlike .gitignore, where
+# this same line matches at any depth) — a bare `node_modules/` missed frontend/node_modules, so
+# `COPY frontend/ ./` overlaid the host's Windows tree on top of what `npm ci` had just installed.
+**/node_modules/
 frontend/dist/
+# Host-only test artifacts. e2e/.auth/state.json is a live Playwright session: it never reached the
+# runtime image (stage 2 copies only /fe/dist), but it has no business in the build context either.
+frontend/e2e/.auth/
+frontend/playwright-report/
+frontend/test-results/
+**/*.log
 backups/
 *.dump
 README.md