Hello, first a battery's capacity is bound to it's volume. therefore a battery with the same form factor can not be 30% stronger and cheaper .... Because a stronger battery in the same form factor would need a more efficient technology which is usually more expensive.
The fact that Ali Sellers write 6800mAhr seems to be that they count capacity in both directions... in and out... this means that the battery probably only has about 3400mAhr.
However i found a battery with a connector at ali. I will order it and look into my Note Air 2 Plus the next weeks and check if it is working.
Best Regards Tom
link to ali battery:
https://de.aliexpress.com/i/4000314326401.html