`.pth` files located in `app_packages` are not processed

### Describe the bug

`.pth` that are located in the `app_packages` folder are not correctly processed on all platforms.

This leads to import errors with some packages. A prominent example is `pywin32` (see [here](https://github.com/beeware/briefcase/issues/381) and [here](https://github.com/beeware/briefcase/issues/835)).

In addition, any Python code can be executed via `.pth` file at startup. This can also be used, for example, to establish a connection with a remote debugger (see [here](https://github.com/beeware/briefcase/issues/2147) and [here](https://github.com/beeware/briefcase/pull/2173)).

The following platforms are affected by this:
- Windows App
- Windows VisualStudio
- Linux Flatpak
- Linux System
- Linux AppImage (I guess, but I am not 100% sure. I could not test this so far.)
- macOS App
- macOS XCode
- iOS XCode
- Web

The following platforms are not affected by this:
- Android (but there is another bug as noted [here](https://github.com/chaquo/chaquopy/issues/1338))

### Steps to reproduce

Add the following to `pyproject.toml`
```
...
[tool.briefcase.app.helloworld]
requires = [
"git+https://github.com/timrid/pth-execution-checker@main"
]
...
```

and somewhere in the app call

```
import pth_execution_checker
if not pth_execution_checker.pth_executed:
raise RuntimeError(".pth file not processed...")
```

### Expected behavior

`.pth` files should be processed correctly on all platforms.

### Screenshots

_No response_

### Environment

- Operating System: Windows, Linux, macOS
- Python version: 3.13
- Software versions:
- Briefcase: 0.3.22

### Logs

### Additional context

One solution would be to remove `app` and `app_packages` entirely and move all packages to `site-packages`, as described in https://github.com/beeware/briefcase/issues/2195. But this was rejected by @freakboy3742. But he made the following suggestion ([Link](https://github.com/beeware/briefcase/issues/2195#issuecomment-2727821874)):

> The site_packages folder isn't inherently special - it's just on the site list by default because it's a location tied to a the Python interpreter's libdir. The method site.addsitedir() exists to add additional site folders - I'm fairly certain the fix here is to use this method to add app_packages as a site dir, rather than just adding it to PYTHONPATH/sys.path as the stub is currently doing.

Start by locating the platform stubs that add app_packages through PYTHONPATH or sys.path, then compare their behavior with Python's site.addsitedir() suggestion. Reproduce the issue using the pyproject.toml dependency and pth_execution_checker example, and verify that .pth files are processed on each affected platform.

Written by the indexing model from the issue text.