I am finding misaligned figure captions when using TeXlive 2021 with amsart. A test file is here:
\documentclass{amsart}
\begin{document}
\hbox to\hsize{X\hfil \TeX{Live} 2021 on Mac\hfil X}
\begin{figure}[h]
\hbox to\hsize{X\hfil X\hfil X}
\caption{XXXXX}
\end{figure}
\end{document}
The first hbox is just to show the margins. Running with TeXlive 2021 (June 2021) on Macosx 11.6, the caption is not centered:
However, running with TeXlive 2019 on Ubuntu 20.04, the centering is correct: I have checked that the part of amsart.cls concerned with figure captions has not changed between these versions. Also, it doesn't make any difference whether latex or pdflatex is used. The problem only occurs for captions that fit on one line.
These are the only two versions of TeXlive that I have easy access to.
\captionindent=0pt
was a reasonable temporary work around for me pending the fix.