Can anyone explain the constant in this relation

When the following function is plotted in desmos,$$y^x = \frac{(xy)^y}{k},$$

Graph where $k = 1$, i.e. $y^x = (xy)^y$.

As k approaches the number $\approx 2.89473713041139$ ($1/k \approx 0.345454511048)$, the graph can be seen to converge at a point.

Graph converging at point.

As well as I can understand, this number doesn't hold any real significance, and so I am wondering what causes this number to make the graph converge. I attempted to use the Lambert W function, but was unable to make any real progress.

Thanks,Nathan