This is another take on #8276, with the same underlying motivation.
However, this approach is mostly duplication-free, which seems better,
especially given the already-pretty-sorry state of our CI config.
Like #8276, this is done in 2 commits for ease of review. The first
commit is wholly unintresting and just copies `azure-pipelines.yml` to
both `ci/prs.yml` and `ci/build.yml`; the second commit removes from
each part what it shouldn't have. The intention is for `ci/build.yml` to
have all of the common parts.
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