MacBook Air 10.15.2 Shuts Down on Startup, falsely indicating 0% battery
I believe the battery in your laptop is shot. It might say it's fully charged, but the internals are no longer sufficiently capable of holding a charge or delivering enough of a consistent supply of electricity to safely run the laptop (to be clear, by "safely", I mean "without it losing power and shutting down", not "without causing harm to you and your loved ones").

I suspect it won't be long before the battery stops saying it's fully charged, and starts displaying an X through the charge level icon.

What you describe is exactly what happened to my old MacBook a few years ago.