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Rollup merge of #131945 - aDotInTheVoid:footnote-time, r=notriddle
rustdoc: Clean up footnote handling
Best reviewed commit by commit.
Extracts footnote handling logic into it's own file (first commit) and then makes that file slightly nicer to read/understand.
No functional changes, but lays the groundwork for making more changes to footnotes (eg #131901, #131946)