Make e2e server spawning work in a git worktree without a hand-made node_modules symlink

[alexeygrigorev]

Raw intake from PM acceptance of #192.

Two e2e specs spawn the test server through an absolute path into the repo-root
node_modules, which does not exist inside a git worktree checkout:

• backend/e2e/frontend-module-characterization.spec.js:141
spawn(path.join(ROOT, "node_modules", ".bin", "tsx"), ["scripts/test-server.ts"], …)
• backend/e2e/planning-surfaces-design.spec.js:97
spawn(path.resolve(__dirname, "..", "..", "node_modules", ".bin", "tsx"), …)

Both are pre-existing and were not modified by #192.

Why it matters

Every agent worktree under .tmp/worktrees/ is a real working tree without its
own node_modules, so both specs fail there with spawn … ENOENT before the
server ever starts. That is the standard pipeline layout: Software Engineer and
Tester both run the full e2e suite from a worktree. During #192 the engineer had
to hand-create node_modules -> /home/alexey/git/dataops/node_modules inside the
worktree just to run npm run test:e2e:backend, and the Tester had to keep that
symlink to reproduce. An untracked manual symlink is not a reproducible harness.

Two secondary consequences seen in #192:

• .gitignore line 1 is node_modules/ with a trailing slash, which matches
  directories only, so the symlink shows up as ?? node_modules in
  git status and is one careless git add -A away from being committed.
• backend/e2e/docs-outage.spec.js (added by Show a docs outage as an outage on the operations surfaces, not as an empty corpus #192) already uses
  spawn('npx', ['tsx', 'scripts/test-server.ts'], { cwd: BACKEND_ROOT }),
  which needs no symlink, so a working pattern already exists in the same
  directory.

Things to settle during grooming

• Whether every spec that spawns a server should use one shared helper rather
  than three hand-rolled spawn call sites (docs-outage.spec.js also has its
  own startServer).
• Whether npx tsx is the right resolution strategy, or a resolved
  require.resolve('tsx/cli')-style lookup that still works when the package
  lives in a parent directory.
• Whether .gitignore should ignore node_modules without the trailing slash
  so a symlinked workaround cannot be staged accidentally, or whether the
  workaround should simply stop being necessary.
• Whether CI is affected at all (it clones a normal repo with a real
  node_modules, so this is a local/worktree reproducibility problem, not a
  CI-red problem).

Verification hints

Reproduce by running npx playwright test e2e/frontend-module-characterization.spec.js
from backend/ inside a fresh git worktree with no node_modules symlink.