MAC dies when I unplug even though battery is charged and healthy.

Sounds like a hardware issue of some sort. Try running the Apple Diagnostics to see if any hardware issues are detected. Unfortunately the diagnostics rarely detect problem even when there is an actual hardware issue, but it never hurts to check.

Try an SMC Reset.

Disconnect all external devices in case one of them is causing a problem.

Try connecting the charger to the USB-C ports on the other side of the laptop to see if that makes any difference. Perhaps there is an issue with one or more of the USB-C ports.

If you have never had the Battery replaced, or the Top Case Assembly (contains the palmrest, Keyboard, Trackpad, Touchbar, Speakers, and Battery), then the battery is probably failing (the condition & cycle count doesn't always reveal the truth).

Personally I would not put any more money into this laptop since it is now considered "Vintage" by Apple and the last supported version of macOS is Big Sur. Your money would be best spent by putting it towards a new computer.

Please help us help you. Our having more details will help get you more effective answers faster.

What macOS version is the computer running?

What activity are you doing when it shuts down? Are you actively using the computer or is it asleep when this happens.

Is a browser is open when this happeds, what browser?

Have you installed any:

• anti-virus software?
• so-called "cleaning," "optimizing," or "tune-up" apps?
• Any client-side VPN (virtual private network) software?