Good point! I will investigate that, even it's not relevant to my chai app I think it's interesting and worthwhile to know if the convert command will do that!
edit: ChatGPT thinks you might be right! It also says: If you specifically need to maintain the vector properties of the EPS file when converting to PDF, you might want to use a tool designed to work with vector formats, such as epstopdf, which is a utility that comes with most TeX distributions.
