Aww OP ... as I am want to say ... you need to slow your roll. Too much, to soon and too fast. And you've overlooked a basic principle. You can't fairly correct a puppy/dog for failing to obey a command, that they don't fully understand.
The goods news is you realized ... what your doing is not working??? So maybe do something different?? That is ... out think your puppy.
We just had a thread on the "Stay" thing and I still train it. Others don't these days, as with a Sit or a Down or a Place Command ... Stay is implied. No doubt that's true but I still train "Stay" for practical reasons but that's another topic.
I don't use treats myself, I found them like you to be a distraction. But that was wayyyy back in the day. But most likely, like you, I overused treats??? These days ... I suppose, I now consider "treats" as a tool and like any tool ... improperly used ... "treats" to can be abused.
Moving on ... I think also, training "Down" first ... is a better way to go?? If the puppy is in a "Down" ... which would need to be trained first, if you say "Stay" it will have more meaning?? Oh not suppose to move??? Soooo I'll do what I know ... "down."
I would also suggest that with "Sit/Stay and Down" you add hand signals! I discovered that to be effective by accident with my Boxer.
You can better see the wheels spinning with those guys.
I'd repeated whatever command, for the umpteenth time and I used a hand signal also. Struddell stared at me like what is dad babbling about??? But she also recognized the hand signal and "Bam" ... instant compliance! Sit Stay Down ... was a piece of cake from that day forward.
But ... now we've just added another command ... "Down" to the list ... which is not exactly helpful??
But fear not ... "Youtube" is your friend, Bethany Wilson, training puppies in Down.:
And of course she has a website and lots of puppy videos.:
That and yes ... a new approach to training your puppy should help ... welcome aboard.