Mirroring test fixes

What does this MR do and why?

Fixes problems with the flaky mirroring tests

• Don't raise an exception if file tree is missing in has_file?
• Factor out code to wait for pull mirroring
• Reload page if the readme isn't found
• Verify mirroring in each mirroring test

See #353900 (closed)

MR acceptance checklist

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• I have evaluated the MR acceptance checklist for this MR.