What is a proportional area chart with a half-circle? Below is a screen grab from https://datavizproject.com/data-type/proportional-area-chart-half-circle/ explaining what it is:
I will go further and say that it actually helps fractions well too. It is one of the reasons why I have chosen to use the basis to visualise the "Impressions" and "Engagements" data in my viz. With the "Impressions" being on top in blue and "Engagements" below in grey, it represents the fraction of "Impressions over Engagements" - the formula to get Engagement Rate. Visualising a fraction this way, I believe helps viewers to get an idea of the proportion of the numerator against the denominator.
However, I will not say that squares are better than circles for such charts. There are reasons why circles are better visually to us as explained here. We have also looked at circles before on this blog, so you can type "circle" in the search bar of this blog to find the posts.
All in all, as an experiment, the use of squares for half-proportional area charts can be described as a possibility, but it may be better to stick with things audiences are familiar with.