Repo configuration: set up pr-dependency-check for dependent pull requests about carbon-lang HOT 4 CLOSED

dpulls is a GitHub app, and "installing" it for our repo/organization involves granting access to a third party. It's also not free for private repositories.

Neither is a deal-breaker. And I'm explicitly not trying to set a NIH precedent where we avoid paying for things that improve productivity. But in this case I'd suggest we look at solving the same problem with a GitHub Action. There is already a step available that looks like we could wire it in: https://github.com/marketplace/actions/pr-dependency-check

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Even better; let's try the action! Retitling the issue

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One concern I have is that landing the dependency PR may not cause the action to re-run for the dependent one, which would be a pain. Testing to find out.

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@mmdriley #343 is ready to test out; I'd like someone to scrutinize the test with me, so if nobody volunteers before then, perhaps when you're back.

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