build(ui): drop redundant tsc type-check from ui build (#8781)

## Thinking Path

> - Paperclip is the open source app people use to manage AI agents for
work
> - CI runs a set of required PR checks; the Canary Dry Run job is the
slowest (~4m)
> - Its dominant cost is `release.sh` Step 2 `pnpm build` (~133s), whose
critical path is the `ui` package
> - In `ui`, `tsc -b` runs ~46s *before* `vite build` (~20s), but
`ui/tsconfig.json` sets `noEmit: true`, so `tsc -b` is a pure type-check
that emits nothing — vite produces all artifacts
> - The PR workflow already runs a parallel Typecheck job
(`typecheck:build-gaps`) that auto-type-checks any workspace package
whose build script omits `tsc`
> - This pull request drops `tsc -b` from the `ui` build so the
type-check moves off the build/release critical path onto the slack-rich
Typecheck job
> - The benefit is ~46s shaved off the slowest PR check with no loss of
type coverage

## What Changed

- `ui/package.json`: `build` script changed from `tsc -b && vite build`
to `vite build`.
- Type coverage is preserved automatically:
`scripts/run-typecheck-build-gaps.mjs` already type-checks any workspace
whose `build` script omits `tsc` and defines a `typecheck` script. With
this change, `@paperclipai/ui` (whose `typecheck` is `tsc -b`) is now
picked up by the parallel Typecheck job. No script edit was required —
the gap-detection is generic.

## Verification

- `pnpm --filter @paperclipai/ui build` produces `ui/dist` via vite
alone (no `tsc` invocation).
- `pnpm typecheck:build-gaps` now type-checks `@paperclipai/ui` and
exits 0.
- A type error in `ui` still fails the parallel Typecheck job, so
type-error coverage is unchanged.

## Risks

- Low. The type-check is relocated, not removed. This is build-tooling
only — no migration, no runtime behavior change. If
`scripts/run-typecheck-build-gaps.mjs` ever stopped covering `ui`, a
type error could slip past the build job — but its gap-detection is
generic (any package with a tsc-less build plus a `typecheck` script),
and `ui` qualifies.

## Model Used

Claude (Anthropic), `claude-opus-4` family, extended-thinking mode with
tool use, operating as an automated CI-health agent.

ui/package.json

@@ -15,7 +15,7 @@
   "type": "module",
   "scripts": {
     "dev": "vite",
-    "build": "tsc -b && vite build",
+    "build": "vite build",
     "storybook": "storybook dev -p 6006 -c storybook/.storybook",
     "build-storybook": "storybook build -c storybook/.storybook -o storybook-static",
     "preview": "vite preview",