While this is likely a hardware issue, Apple tends to over do things. There are people with the skills to repair the logic board Vs replacing it.
Let’s dig a bit deeper to see if we can identify what the issue is. Install this gem of an App [https://www.coconut-flavour.com/coconutbattery/|CoconutBattery] post a snapshot of the Apps main window here so we can see it as well.
Also where do you live? Country and nearest major city. Maybe we can aim you to someone local to you who is a lot cheaper than what Apple was asking.