How would you add sequentially numbered labels to images in posts?

No need for plugins or any change to the markup – you can do all of this in pure CSS with what is called counters, which do have broad browser support.

body {
  counter-reset: imageLabel;
}

.wp-block-image::before {
  counter-increment: imageLabel;
  content: "#" counter(imageLabel);
}

This will already produce the number after the image, you can style the ::before however you like and position it where it needs to be.

Beware that this might hurt the accessibility of the page, I’m unsure how well screen readers can interact with both ::before and the CSS content. However, solving this will probably require you to create either a new block or edit the image block .