Still working on this, I'll see if I can finish this and open it for review by the end of today.

Did a redesign and this seems to be a better implementation than the last. Just need to add coverage tests then I'll open this PR for review

I think this is ready to go, going to open this for review

Here are my design decisions:

• Decided to keep the warning printing logic in their respective modules since they appear to be tightly coupled together
• Included a _warning module; did try to add it to render but I encountered dependency cycle errors
• Implemented a WarningPrinter class, where I also exposed a shared module-level singleton of it
• Decided that the duplicate metadata warning should not be considered a "fail" warning when --warn fail is passed. My reasoning for this is that Python allows these duplicate distributions to exist and pip actively ignores them.
• I thought it would be nice for WarningPrinter.print_multi_line() to pass what file to write to to the callback so that we avoid throwing sys.stderr everywhere, but due to an odd long-standing bug with the capsys/capfd fixtures, it won't properly capture sys.stderr if we were to pass it down to the callback.

Ignore my previous deleted comment, I've reconsidered and the handling of "duplicated" here should be fine.

No questions for me here. But I don't have the approve auth, so maybe need to wait for @gaborbernat to take a further look.

Great, will release 2.19.0 after merging this