Debug Breakpoint are not triggered in Web Exports

### Tested versions

- 4.4 dev2

### System information

MacOS , Windows 11

### Issue description

When running a Godot project from the editor targeting a web export, the running game on the browser successfully connects with the debugger, but breakpoint functionality is not working.

All other debugging features (Profiling, Monitors) are supported and functioning correctly.
However, breakpoints are never triggered.

### Steps to reproduce

- Open a Godot project.
- Set a breakpoint in any script.
- Enable Remote Debug from the Debug menu.
- Run the project from the editor with a web export target.
- Observe that the game connects to the debugger, but breakpoints are not triggered.

### Minimal reproduction project (MRP)

[WebDebug.zip](https://github.com/user-attachments/files/17162815/WebDebug.zip)

Start with the provided WebDebug.zip reproduction and follow the editor's Remote Debug path when running a web export. Confirm the browser connects and profiling and monitors work, then trace why a script breakpoint is not triggered; done means breakpoints trigger during web-export runs.

Written by the indexing model from the issue text.