[browser-esbuild] live-reload=false workflow is less convenient now

### Command

serve

### Description

I often work with `live-reload` disabled. This is helpful when working on CSS changes, I can try things in browser and then make multiple edits in files before manually reloading.
It's also faster when working on a laptop.

Before esbuild:
1. Make changes.
2. Refresh page.
3. Page reloads after new changes have been compiled.

With esbuild:
1. Changes.
2. Refresh.
3. Page reloads immediately before changes have been compiled. Now I need to monitor terminal and reload the page after successful compilation.

### Describe the solution you'd like

I was okay with the old behaviour where server wouldn't respond before successful compilation.

A less desired alternative would be to log Vite messages in browser's console, so that I can tell when compilation has finished there.

### Describe alternatives you've considered

_No response_

Start with the `serve` command's `live-reload=false` workflow and trace how browser requests behave while esbuild compiles changes. Reproduce the refresh sequence, then verify that a refresh waits for successful compilation or that compilation completion is surfaced in the browser console.

Written by the indexing model from the issue text.