[mobile] Add Android NuGet BrowserStack test to NuGet packaging pipeline (#23580)
### Description
Follow-up to #23551
Adds the BrowserStack testing stage for Android to the NuGet packaging
pipeline.
This test tests that the NuGet package produced will be imported and
work correctly on an Android device
[Pipeline run that shows what a failing unit test would look
like](https://aiinfra.visualstudio.com/Lotus/_build/results?buildId=670961&view=results)
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Co-authored-by: Edward Chen <18449977+edgchen1@users.noreply.github.com>