It’s not so interesting I think.

They’re basically just taking equations of the form f(x,y)=k where k=0, and asking “ah but what about when k!=0”?

Indeed, looking at the constant as a variable by looking at the equation f(x,y)=z IS quite useful. (I’m reminded of Feynman favorite trick for solving integrals). That generalization trick is actually useful in MANY contexts. But there’s nothing novel here.