Cannot support non-standard location for `.android` directory

### Describe the bug

The default location for the Android SDK's `.android` directory is `$HOME/.android` but it can be an arbitrary directory via `ANDROID_USER_HOME`. When Briefcase creates an AVD, it tries to modify its configuration afterwards; this fails because it assumes the AVD is located within `$HOME/.android`. More generally, enumerating the list of AVDs assumes this location as well.

### Steps to reproduce

Run `ANDROID_USER_HOME=/tmp/android briefcase run android` and create a new emulator.

```
❯ ANDROID_USER_HOME=/tmp/android briefcase run android -vv
Using JDK at /home/russell/.cache/briefcase/tools/java17
Using Android SDK at /home/russell/.cache/briefcase/tools/android_sdk
Android emulator is already installed.

>>> Running Command:
>>> /home/russell/.cache/briefcase/tools/android_sdk/platform-tools/adb devices -l
>>> Working Directory:
>>> /home/russell/tmp/beeware/helloworld
>>> Command Output:
>>> List of devices attached
>>>
>>> Return code: 0

>>> Running Command:
>>> /home/russell/.cache/briefcase/tools/android_sdk/emulator/emulator -list-avds
>>> Working Directory:
>>> /home/russell/tmp/beeware/helloworld
>>> Command Output:
>>> beePhone
>>> Return code: 0

Select device:

1) @beePhone (emulator)
2) Create a new Android emulator

> 2

>>> Running Command:
>>> /home/russell/.cache/briefcase/tools/android_sdk/emulator/emulator -list-avds
>>> Working Directory:
>>> /home/russell/tmp/beeware/helloworld
>>> Command Output:
>>> beePhone
>>> Return code: 0

You need to select a name for your new emulator. This is an identifier that
can be used to start the emulator in future. It should follow the same naming
conventions as a Python package (i.e., it may only contain letters, numbers,
hyphens and underscores). If you don't provide a name, Briefcase will use the
a default name 'beePhone2'.

Emulator name [beePhone2]:
Device skin 'pixel_7_pro' already exists.

>>> Running Command:
>>> /home/russell/.cache/briefcase/tools/android_sdk/cmdline-tools/9.0/bin/avdmanager --verbose create avd --name beePhone2 --abi x86_64 --package 'system-images;android-31;default;x86_64' --device pixel
>>> Working Directory:
>>> /home/russell/tmp/beeware/helloworld
>>> Environment Overrides:
>>> ANDROID_HOME=/home/russell/.cache/briefcase/tools/android_sdk
>>> ANDROID_SDK_ROOT=/home/russell/.cache/briefcase/tools/android_sdk
>>> JAVA_HOME=/home/russell/.cache/briefcase/tools/java17
>>> Command Output:
>>> Loading local repository...
>>> [========= ] 25% Loading local repository...
>>> [========= ] 25% Fetch remote repository...
>>> [=======================================] 100% Fetch remote repository...
>>> Return code: 0
Creating Android emulator beePhone2... done
Adding extra device configuration... errored

Unable to read configuration of AVD @beePhone2

```

### Expected behavior

Briefcase respects `ANDROID_USER_HOME` or similar.

### Screenshots

_No response_

### Environment

- Operating System: pop os 22.04
- Python version: 3.10
- Software versions:
- Briefcase: `0.3.18.dev72+ge141754e`

### Logs

[briefcase.2024_02_24-16_41_28.run.log](https://github.com/beeware/briefcase/files/14394489/briefcase.2024_02_24-16_41_28.run.log)

### Additional context

_No response_

Reproduce the issue with ANDROID_USER_HOME=/tmp/android briefcase run android and trace Android AVD creation and enumeration. Check the paths used after avdmanager creates an emulator and when listing AVDs; done means both operations respect the configured directory and the reported configuration can be read successfully.

Written by the indexing model from the issue text.