[AI] Address review feedback for browser API build

- Remove `internal` export from index.web.ts (keep as local variable)
- Use `yarn build:node && yarn build:browser` in build script
- Remove unnecessary `node:` external from vite.browser.config.ts
  (Vite handles browser externalization automatically)

https://claude.ai/code/session_01MnxRXLNjqXrVb5CdsC85Fb

packages/api/index.web.ts

@@ -4,8 +4,7 @@ import type { InitConfig, lib } from '@actual-app/core/server/main';
 export * from './methods';
 export * as utils from './utils';
 
-/** @deprecated Please use return value of `init` instead */
-export let internal: typeof lib | null = null;
+let internal: typeof lib | null = null;
 
 export async function init(config: InitConfig = {}) {
   internal = await initLootCore(config);