What kind of wordplay is this?

Puns rely on a range of phenomena that lie somewhere between polysemy and homophony. However, polysemy is a rather complex and fuzzy phenomenon so it's not a perfect fit.

All your examples are cases of polysemy such as 'budding genius'.

But a homophonic pun would be something like "Atheism is a non-prophet institution" or more on the homographic side "You need to Czech Prague out."

However, the question is what makes the puns you list work is something you might call semantic frame dissonance caused by polysemy of words in the punchline that fit into the semantic frame triggered by the set up. For instance, words like 'gush' belongs to the frame of oil extraction but it is not being used in the sense that fits with the frame. Thus the humorous effect. The same is the case with a florist having a budding genius and a blooming idiot for children.

Instead of semantic frame you could talk about 'semantic fields' or you could also conceive of some of the cases as simply collocations.

I think it is this kind of relatedness that made the author talk about synonymy but words like oil well and gush are not synonyms, they are simply semantically related.