Run `check_contrib()` once, declare as dependency of html/pdf/epub/mobi

[HonkingGoose]

The process could be improved by only running check_contrib() once (by declaring it a dependency of html/pdf/epub/mobi). But it is out of scope of this PR.

Originally posted by @slonopotamus in #1656 (comment)

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Link to rake file we need to change: https://github.com/progit/progit2/blob/main/Rakefile

[HonkingGoose]

Todo for after PR #1656 is merged.