CI: Add an integration test that runs the entire backporter script

[DilumAluthge]

Obviously it's better to have unit tests whenever possible, but at least this integration test can serve as a basic sanity check that a PR won't break the script.

[codecov-commenter]

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Codecov Report

❌ Patch coverage is 0% with 21 lines in your changes missing coverage. Please review.
⚠️ Please upload report for BASE (master@7e221b2). Learn more about missing BASE report.

Files with missing lines	Patch %	Lines
test/integration.jl	0.00%	21 Missing ⚠️
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Additional details and impacted files

@@            Coverage Diff            @@
##             master      #30   +/-   ##
=========================================
  Coverage          ?   24.15%           
=========================================
  Files             ?        7           
  Lines             ?      832           
  Branches          ?        0           
=========================================
  Hits              ?      201           
  Misses            ?      631           
  Partials          ?        0           

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[DilumAluthge]

@IanButterworth What do you think of this one? It might be a nice way to catch breakages in PRs.

[DilumAluthge]

Oh, we would need to decide whether we want to:

1. Only upload Codecov info for the unit tests
2. Upload Codecov info for both the unit tests and integration tests. Obviously, this will make the Codecov number look higher, but it might be misleading, because a good portion of that higher coverage number would be from the integration tests, which aren't really testing much, just that we can run the entire script without error.