chore(FR-2851): drop deprecated/dead babel deps and dead babel.config.js (#7321)

Resolves #7320(FR-2851)

## Summary

Three direct dependencies print `deprecated` warnings on every `pnpm install`. This PR retires them, and while we're in the file, deletes the dead `babel.config.js` they were tied to plus the four root babel plugins it was the sole consumer of.

### Direct dep changes

- `react/package.json`: `@babel/plugin-proposal-private-property-in-object` → `@babel/plugin-transform-private-property-in-object` (Babel 7.13+ rename, drop-in re-export).
- Root `package.json`: removed
  - `babel-eslint` — dead. ESLint 9 flat configs (`eslint.config.mjs`, `react/eslint.config.js`, `e2e/eslint.config.mjs`, `packages/backend.ai-ui/eslint.config.js`) all use `@typescript-eslint/parser` + `@eslint/js`; `grep -rn babel-eslint` returns zero hits.
  - `@babel/plugin-proposal-class-properties` — only ever referenced from `babel.config.js`, which is dead (see below).
  - `@babel/plugin-proposal-decorators` — same.
  - `@babel/plugin-syntax-dynamic-import` — same.
  - `@babel/parser`, `@babel/types` — no consumer in `src/`, `scripts/`, `electron-app/`, `packages/`.
- Root `babel.config.js`: deleted. After the CRA→Vite migration, no build path reads it: `@vitejs/plugin-react` defaults to `configFile: false`/`babelrc: false` and both `react/vite.config.ts` and `packages/backend.ai-ui/vite.config.ts` configure `babel.plugins` inline (`babel-plugin-react-compiler` + `babel-plugin-relay`). `tsup` (used by `backend.ai-client`) uses esbuild, not babel. There is no `babel-loader`, `@babel/register`, or `babel-node` consumer in the repo.

### Why now

Every contributor sees these three warnings on `pnpm install` and has no way to silence them without editing a direct dependency. The `babel.config.js` next to them was orphaned and pinning four real packages for nothing.

## Lockfile diff

The lockfile shrinks ~10K lines. The shrink is mostly from `babel-eslint`'s 2019-era transitive chain dropping out, but it also drops a few entries that were already orphaned in `main`'s lockfile from the CRA→Vite migration (`react-scripts` patch chain, `@craco/craco`, etc.). These had no live consumer; `pnpm install` simply re-resolves them out. No behavior change.

The legacy `plugin-proposal-class-properties@7.18.6` and `plugin-proposal-private-property-in-object@7.21.11` entries that remain in the lockfile are pulled in transitively by `babel-preset-react-app@10.1.0` (still a `react/` devDep). Removing that preset is out of scope for this PR but a reasonable follow-up — it would also let the renamed `transform-*` direct dep in `react/package.json` go away.

## Verification

- `pnpm install` no longer prints `deprecated` warnings for `babel-eslint`, `@babel/plugin-proposal-class-properties`, or `@babel/plugin-proposal-private-property-in-object`.
- `bash scripts/verify.sh` — Relay / Lint / Format pass. The TypeScript failures shown (`packages/backend.ai-client/src/client.ts` implicit-any, `DeleteForeverVFolderModalV2.tsx` `BulkPurgeVFoldersV2Input.options`) are **pre-existing on main** (verified by re-running with my changes stashed), unrelated to babel deps.

## Test plan

- [ ] `pnpm install` shows no deprecation warnings for the three packages above.
- [ ] `pnpm run dev` starts the dev server without runtime errors related to babel transforms.
- [ ] CI passes the same set of checks that pass on `main`.

Author: yomybaby

babel.config.js

@@ -47,12 +47,7 @@
   },
   "devDependencies": {
     "@babel/core": "catalog:",
-    "@babel/parser": "^7.29.0",
-    "@babel/plugin-proposal-class-properties": "^7.18.6",
-    "@babel/plugin-proposal-decorators": "^7.29.0",
-    "@babel/plugin-syntax-dynamic-import": "^7.8.3",
     "@babel/preset-typescript": "catalog:",
-    "@babel/types": "^7.29.0",
     "@electron/packager": "^18.4.4",
     "@eslint/js": "catalog:",
     "@jest/expect": "catalog:",
@@ -67,7 +62,6 @@
     "@typescript-eslint/eslint-plugin": "^7.18.0",
     "@typescript-eslint/parser": "^7.18.0",
     "@yao-pkg/pkg": "^6.14.1",
-    "babel-eslint": "^10.1.0",
     "buffer": "^6.0.3",
     "cli-color": "^2.0.4",
     "concurrently": "^8.2.2",