Should I include proof of my extenuating circumstances when applying for a PhD?

You might mention extenuating circumstances if:

• They significantly decreased your past performance.
• You explain why your performance will not be reduced in the future for the same reason.

Do not include any evidence unless it is requested, or perhaps if the circumstances were something very unlikely. Having been imprisoned for a crime and later exonerated might be an example where evidence would be a good idea.

Since you are now in an MS program now and are doing better at it, I think it would be a mistake, actually, to dwell too much on the reasons for poor performance earlier. At most, a single phrase in an application letter that you suffered physical injuries as an undergrad that impacted your performance at the time. No more than that.

Applications will put heavier weight on later work over earlier in any case and people improve their work for many reasons. If it were the later work that was impacted, you might need more explanation. But in this case, just a hint that someone can follow up on if they think it necessary, is plenty.

I wouldn't attach any diagnostic report. But you could highlight, that you're especially proud of your performance increase during your masters, because it was closely linked to you overcoming the health issues you endured during your bachelors degree. But only use one sentence for this, it shouldn't be more than a side note.

Definitely don't make it sound like you want special treatment because of your past health problems, but instead present the way you coped with them as a strength. To overcome serious illness shows that you are capable to overcome setbacks, this is very valuable.