chore: Replace prettier with oxfmt (#8177)

Configure oxfmt ignorePatterns to exclude non-JS/TS files (md, json,
css, yaml, etc.) to match previous Prettier behavior.

┆Issue is synchronized with this [Notion
page](https://www.notion.so/PR-8177-chore-configure-oxfmt-to-format-only-JS-TS-Vue-files-2ee6d73d3650815080f3cc8a4a932109)
by [Unito](https://www.unito.io)

---------

Co-authored-by: Amp <amp@ampcode.com>

AGENTS.md

@@ -27,10 +27,10 @@ See @docs/guidance/*.md for file-type-specific conventions (auto-loaded by glob)
 - Build output: `dist/`
 - Configs
   - `vite.config.mts`
-  - `vitest.config.ts`
   - `playwright.config.ts`
   - `eslint.config.ts`
-  - `.prettierrc`
+  - `.oxfmtrc.json`
+  - `.oxlintrc.json`
   - etc.
 
 ## Monorepo Architecture
@@ -46,7 +46,7 @@ The project uses **Nx** for build orchestration and task management
 - `pnpm test:unit`: Run Vitest unit tests
 - `pnpm test:browser`: Run Playwright E2E tests (`browser_tests/`)
 - `pnpm lint` / `pnpm lint:fix`: Lint (ESLint)
-- `pnpm format` / `pnpm format:check`: Prettier
+- `pnpm format` / `pnpm format:check`: oxfmt
 - `pnpm typecheck`: Vue TSC type checking
 - `pnpm storybook`: Start Storybook development server
 
@@ -72,7 +72,7 @@ The project uses **Nx** for build orchestration and task management
     - Composition API only
   - Tailwind 4 styling
     - Avoid `<style>` blocks
-- Style: (see `.prettierrc`)
+- Style: (see `.oxfmtrc.json`)
   - Indent 2 spaces
   - single quotes
   - no trailing semicolons