CoconutBattery app shows different battery state of charge then the built in app

100% support for John Galt's comments.

Your MacBook is a mass produced device, and its sensors are not individually calibrated. Measurement of state of charge and state of health are notoriously difficult to achieve, but state of charge (about 60% in your example) is rather easier and more accurate than overall health and maximum capacity. It will also vary a little from day to day depending on things like temperature. As a general guide I wouldn't expect the state of health estimate to be any better than +/- 5% at best, and I would expect Apple estimates to be usually more accurate than third party software.

The better guide for battery health is what happens to the estimate over a period of months. I would expect the trend will be a slow fade from <condition as new>, but I'm not going to predict future numbers because it depends how you use the device and how it gets charged. Like John Galt I think you will find there is nothing wrong with the battery in your MacBook and you will get years of satisfactory service from it.

There is nothing wrong with that Mac's battery. To learn about Mac batteries please read Get help with your Mac laptop battery - Apple Support.

And he's just slowly dying

New batteries begin life at 100% capacity. It does not increase from there.

If you do not like what you see in the "Coconut Battery" product then I suggest you uninstall it. Whatever the reason for the discrepancy Apple will not be interested in it. If you have questions about that product ask its developer: Contact a third-party vendor - Apple Support.

Enjoy your new Mac!