Sadly it does sound like the charging control logic is messed up.
I’ve seen this quite a few times. Every time I slide the battery into my spare Fn system I can get it recharged enough to test. I install [https://www.coconut-flavour.com/coconutbattery/|CoconutBattery] to see what it tells me often I see an old battery or the sensors are not reporting properly.
As you don’t have a spare system to check things, you’ll need to seek help from an independent shop who has Mac circuit board repair skills.
I’ve replaced a few Renesas (formerly Intersil) ISL9239 battery charger chip which you can see here on Step 17 [guide|72415] in the second image.