fix(bundle): fix vite build

Some bundlers (like vite) do not support having a "browser" field in a
nested package.json.

Note: the previous commit ([1]) fixed the resolution of the "browser"
field in the dev bundle, but the production bundle still failed.

Related: https://github.com/socketio/socket.io-client/issues/1504

[1]: https://github.com/socketio/engine.io-client/commit/49719142f65e23efa65fca4f66765ded5d955972