Should you tell them?
Well I'll take the role of the potential employer here. In my head the things I want to hear from you is what you will offer me in exchange for me paying you. Frankly, if it doesn't have an impact on that I don't care.
That said if it could potentially affect you at work you might want to say something just so I know, if not it's probably not relevant.
You sir, are NOT an underachiever. You are pursuing a PhD which implies you have at least a Bachelor's degree (or equivalent). That's better than a large portion of the population. In addition the normal time it takes to earn a "four year degree" it five to six years. (because of mistakes in scheduling, failing a class, taking time off, change in major, etc) so a kid who goes straight from high school to college and powers through should get their degree around the age 24 to 26.
A year or two older than that is not a surprise at all, it happens. So stop beating yourself up, you did better than a significant percent of the population while also suffering from a debilitating health issue.
What should I say?
As a potential employer I don't care if you got you degree in four years or ten years, if you got it, you got it. Your GPA? Don't care... Extracurricular activities? I only care if they are relevant to what I'm hiring you to do. (Say if you were active with Society of Mechanical Engineers and I'm hiring you as a Mechanical Engineer) If not, no problem that's pretty common.
On your resume just put "Earned [Name of Degree] from [Name of School] on [Year Earned]"
Lack of experience
This is the real hurdle to jump, but it's one the vast majority of fresh from school people deal with. The challenge here is people want experience in order to hire you, but you can't get experience unless they hire you.
This is where many fresh out of school kids stumble. Most of our parents engrained the idea that if you don't get a degree you're digging ditches or flipping burgers, if you get a degree you get a job easy! (which was true at one point) These days though you're competing with EVERYONE who also got their degree.
You have to be very careful to shoot for a job that both challenges you, but is not impossibly beyond your abilities. (No matter how good or bad you were at school the safe assumption is you're "entry level" your ideal company is one that will invest time and effort into helping you get better and learn more, or put you in a team where someone with more experience will guide you)
The best ways to find these jobs are local job fairs, if your school has a job placement program those are good, asking others in the industry in your area for places that people use to launch their careers, visiting whatever professional events / community is near you as often recruiters frequent these events, or if all else fails hit up places like career builder or linkedin. (For warning in person resources are reliable, you REALLY need to vet stuff from the internet, the online stuff is a mixed bag of good opportunities, scams, and places to work that will suck all motivation and desire from you leaving you an empty husk of sadness and despair.)