This answer is answered by this CBS/YouGov poll:Who won? Will it help any candidate?
The June 9th numbers were just a month before the debate. The only major thing that occurred after June 9th was the debate so I think it's reasonable to say that the uptick and negative numbers for Biden had to do with his debate performance. Even then, having 65% of voters thinking that you don't have the cognitive health to be president is pretty bad. And Trump has about 50% of voters that think he does not have the mental health to be president.
Here's even more relevant polling on the debate performance from the same source:
If this does not convince voters that we need more options, even beyond the two-party monopoly that we have, then I don't know what will.