chore(web): format-gate the ungated first-party TS/JS (server/, vite.config.ts, scripts/) #1778

Summary

clients/web's format:check is scoped to src/ (prettier --check src), and the root format/format:check covers core/ plus each client's own scope. Nothing prettier-checks:

• clients/web/server/** (Node dev/prod backend + Vite config helpers)
• clients/web/vite.config.ts
• scripts/*.mjs (root build/verify tooling)

So formatting in those files isn't gated by validate / CI. It's a pre-existing gap, surfaced repeatedly during the review of #1769 / PR #1777 — that PR alone adds a ~240-line scripts/verify-build-gate.mjs and a new clients/web/server/ module to the ungated set, and their quote/wrap style had to be matched to siblings by hand.

eslint already reaches wider (clients/web's lint is eslint ., and the root lint:core covers core/), so this is specifically about prettier coverage — though the two config surfaces should be reconciled together.

Proposal

Extend the format gate to cover the currently-ungated first-party TS/JS:

• Widen clients/web's format / format:check beyond src/ to include server/, vite.config.ts (and any other top-level config it owns).
• Add a root-level prettier scope for scripts/**/*.mjs (mirroring how format:core / lint:core gate core/), wired into validate:core or a new validate sub-step.
• Run prettier --write once to normalize the newly-covered files, then confirm npm run validate / npm run ci stays green.

Notes

• Keep it prettier-only in scope unless the eslint surfaces obviously need reconciling at the same time.
• No runtime behavior change — pure formatting + gate wiring.
• Discovered during the review of PR build(web): fail vite build on a browser-externalized Node built-in (#1769) #1777 (Build gate: fail vite build on a browser-externalized Node built-in (SEP of #1615) #1769).