There is still a slim chance it could be the connecting cable. This cable sometimes is very difficult to connect properly and seems to slip out more often (at least on the 2020 Intel model I just recently worked on), than the older models...I haven't worked on too many Apple Silicon Macs yet. I would recommend a tech actually use Kapton Tape to hold the cable in place even though the connector does have a locking lever...I don't think the locking lever is sufficient on their own. In fact, Apple has a bit of adhesive on the cable tab to hold the cable to the connector to help prevent it from dislodging in case any jarring movement while transporting the laptop causes the cable to wiggle loose...once the cable is disconnected, it never holds as well (a new cable would have a fresh adhesive strip).
Assuming the replacement Battery or Cable is not the issue, then the next logical part would be a defective Logic Board. Unfortunately with these newer Macs it really is not easy to troubleshoot them like it was with the older non-Retina models. It is not easy just to slip in a new battery for testing since the battery is part of the larger Top Case Assembly which includes the Keyboard, Trackpad, Palmrest, Speakers, and Battery (the battery is glued to the underside of the Palmrest & Trackpad)....the whole laptop must be dismantled to test another battery. With an AASP, this is not even possible these days since if the battery is not needed, the AASP is no longer able to return the unused diagnostic part to Apple for a refund anymore. I can tell you from personal experience supporting thousands of our organization's Apple laptops....they are no longer easy to diagnose, nor is it easy to be certain the suspect part will be the one.
So please go easy on your AASP....they are replacing the most logical parts assuming they have looked for signs of accidental liquid damage. I always do so since so many of our organization's users tend to have accidents, but even when I check I can miss a sign especially if I do not remove the Logic Board to examine its hidden side which is exposed to the underside of the Keyboard and prone to liquids (even just a drop) from leaking through from the keys.
Just make sure to keep going back as soon as you see a problem so that if they need to replace the same part again, it will be covered by the 90 day part warranty.
Good luck.
