Battery is dead or is this a fixable issue?

DerpBae wrote:

Full Charge Capacity: 2607 mAh

Design Capacity: 4790 mAh

54.4%

This clearly shows your Battery is at 54% of its original Design Capacity which is terrible. I'm sure the battery cells have a lot more issues as well which is also clearly indicated by the laptop powering off within seconds of disconnecting the power adapter.

Cycle Count: 301

Cycle Count is irrelevant unless it is nearing 1,000 cycles. The age of the battery is more critical than the Cycle Count.

This is with it plugged in and Macbook is telling me to get the battery serviced.

When you are having battery related issues and the battery condition is "Service Recommended", then it means you should have the battery replaced. If you see "Service Recommended" and the battery is still performing to your expectations, then you can ignore the "Service Recommended" condition until the battery no longer performs to your expectations.

Usually most Apple Lithium Batteries begin to wear out or fail between 3 - 5 years although there are always exceptions (nearly 25 years of observations of thousands of my organization's Apple laptops). According to your posted system details, you have gotten almost 6 years of use out of this battery. Seems like you made out very well with it.

Your Mac needs a replacement battery.

Mac Repair and Service - Apple Support

Batteries are a wear item, like the soles of your shoes and the tires on your car. Their expected lifetime depends on use (as reflected in Charge cycles) and also in the passage of time, used or not. After a while, you should expect to have to replace the battery.

Battery life also depends on two factors you may be able to control a bit better. Lithium polymer batteries deteriorate when they get too hot, and when they are subject to very deep discharge. These should be avoided when possible.

Despite using these batteries in millions of Apple devices, there is still a lot of of randomness in exactly which battery will fail when.

Apple SUGGESTS (but does not Warrant) that your battery MAY last as long as 1000 charge cycles, provided all other factors are well-controlled.

Apple uses the criterion that a battery that doesn't to hold 80 percent of its original charge capacity should be serviced, and likely replaced.

When designing systems, that 80 percent rule is intended so that, over a Very large sample of devices, almost all will be able to achieve their 'mission' -- still have at least 80 percent capacity at the three-year mark.