Fixing wrapfig caption alignment?

You are not going crazy!

\documentclass{amsart} is the culprit.

With standard article class everything works fine.

Can you change the class? Maybe updating ams packages helps? Somebody more involved with ams classes should help.

I'm using acmart, which behaves similarly. Here's how I've adjusted things, something along these lines should work for you.

\usepackage{caption}
\DeclareCaptionLabelFormat{mywraplabel}{\hspace{.5ex}#1~#2.\newline}
\captionsetup[wrapfigure]{labelformat=mywraplabel,%
labelsep=none,name=Figure,justification=centering}

Credit where credit is due, the top answer here gives the main clue: How to change spacing between caption numbering and text?