Has Apple indicated that some 2019 MacBook Pros have a fault relating to power, battery or shutdown issues?
At this stage it's too early in the product cycle for this model to know if this rates as a known issue for Apple. 

However, any product, no matter the type or manufacturer, can have a fault and having bad batches of components is not unheard of. Apple does use warranty extension programs, replacement programs and repair programs if/when it identifies there's a definite issue to address. At this stage though it would be pure speculation, even if a handful of MacBook Pros presented with the same issue.

You indicate you've reset the SMC as per Apple's instructions, but just to be thorough your model MacBook Pro has a T2 chip and you have two options for resetting the SMC (the 2nd to be tried if the first fails).

Resetting the SMC on a 2019 MacBook Pro


Fully shut down your MBP. 
Press and hold the power button for at least 10 seconds
Let go of the power button and wait 5 seconds
Power up your MBP again


Once you've reset the SMC fully charge your MBP and see how you go. If it's still misbehaving, reset the SMC again but with the following steps instead:


Fully shut down your MBP. 
Press and hold the right shift key and the left option and control keys for 7 seconds before then also pressing and holding the power button (or Touch ID button) down for another 7 seconds (i.e. the keys will end up being held down for 14 seconds, the power button for 7 seconds)
Let go of all three keys and the power button
Wait 5 seconds
Power up your MBP again


Now test your MBP again.

If the above fails, then I'd be talking to Apple Support to explain what's happening. If they can't address the issue then you're entitled to a refund or replacement, but you'll want to get onto it straight away so that a case is logged this early in your ownership.