As they say, no one ever says "I wish I'd spent more time in the office" on their deathbed. Instead, they say "I wish I'd spent more time with my family/hobbies/traveling/etc." Do these people also wish they'd earned more and learned more? Quite possibly, but does that really matter? IDK.
My answer really starts here, though:
But, looking back, I feel like I should have invested my free time in meeting new people, learning more about public speaking, should have taken leadership positions and should have invested my time in doing things that would have improved my CV. In short, doing things outside my comfort zone.
What's preventing you from continuing to learn on your own? There are plenty of places to learn things online or IRL. There are even places online as resources for IRL learning. One of them is MeetUp.com, where you can get together with people with your own interests and do that interest. This includes computer sciences, talking over coffee, book clubs, electronics, aviation, public speaking, dog walking, whatever. Your local public library might have information on local clubs, too. Some of them might even meet at the library.
You specifically mention public speaking, so find a local Toast Masters club. Maybe find a club that's into your hobbies and make presentations to the club about the hobby. Use the skills you currently have to build up or reinforce the skills you don't have.
Better yet, find a local non-profit and become a Board member. This will help with all kinds of things on your regret list: public speaking, leadership activities, meeting people, improving your CV, and much more. From grant writing to budgeting, running committees to debate, conflict resolution to managing project, being a Board member will teach likely you how to do a little bit of everything and tax what you think you're already learned.
Your real question was "How can I cope up with the regret about my failure of doing things that would have helped me academically and in industry?" Well, do the things now that you didn't do before. Then your regret will be severely undermined due to you actively doing what you regret not doing. It's hard to regret doing something 10 years ago when you did it 2 years ago. It might not fix your feelings immediately, but it will help in the future.
As another Answer mentioned, the hobbies you do during your PhD probably kept you from burnout and likely allowed you to stay sane to complete your degree. This is very good and not to be regretted. If you had "done all the things" while in your degree plan without time to relax and enjoy yourself, you might very well have quit and then you'd have a major regret. I'm not saying this hypothetical situation reduces your current regret, but take some solace in the fact that you don't regret not having finished the degree. Sometimes seeing a worse side of things can make your current burden feel a little lighter.
"But did you die? No? Well there's that." That might be a little harsh, but sometimes you have to be happy you're still "on the right side of the grass." :-)
Good luck, happy trails, and hopefully you found something useful in all the myriad of answers here!