Many newer laptops with mini chargers absolutely need the battery to provide extra power when the cpu clocks up. Also most units now use both an age & genuine check. If the battery wasn’t “fresh”, you’ll have all the problems you described. It’s not the actual battery cells that are bad, probably bad data on the “on battery computer”. Batteries aren’t dumb anymore, they have their own data and safety processor.
I used to rebuild batteries & reprogram them as certain computers could never recognize a “replacement”.
I know there are some battery utilities out there to update the date & recalibrate the unit. Probably not an option, but there may be one out there.