I want to overlay some micrographs with labels (like A, B, C) and arrows to generate a multi-panel figure.

Why not write a PostScript file by hand and put the binary image data in there?

This should make it easy to add the labels and arrows by hand.
Interestingly, I could not find information or tutorials about this, although I would expect this to having been a common practice in the 90ies and I'm surprised that this practice would have gotten extinct by now.

Publishers commonly accept eps (and PDF) files, whereas support for other file formats like SVG varies.

Why should I buy and learn proprietary GUI software like Adobe's Illustrator or Indesign for this purpose only?

For plotting data, I would of course use libraries like matplotlib or R's ggplot.

SVG would be a modern option, but getting bounding boxes of text to align it requires JavaScript or other additional tricks.

Inkscape is nice, but writing PostScript feels more reproducible and automatizable to me.

Yes, there would be only short parts of PostScript code for the vector items (labels and arrows) and long chunks of binary (hex) data in between.