Chosen Solution
I have been using this Late 2012 Macbook Pro Retina for almost 6 years. Battery service already came, never mind, started using with charger always, battery support for 2 hours. Recently I have updated Catalina (from Mojave), not able to login, again re-formatted, Installed Mojave, started to use since then. Fan run loudly, Keyboard backlight not working, sluggish performance… When I do SMC reset, can see charger indicator status change, but no change even after restart. From sleep mode, it goes off, then restart, again fan louder. When battery fully discharged (like 2hrs after), SMC reset, then all works fine as normal. Like to hear from experts to support me… Appreciate your help !!
Sadly the battery need to be replaced ;-{ Batteries die from excessive cycles or just by age. In your case the battery age has caught up with it. MacBook Pro 13" Retina (Late 2012-Early 2013) Battery and here’s the guide: MacBook Pro 13" Retina Display Late 2012 Battery Replacement