Tesseract OCR has a command-line utility which is woefully under-documented. Thanks to Alexandru Nedelcu I figured out how to use it today.
To install on macOS:
brew install tesseract
To convert an image into an annotated PDF (which you can then copy and paste text out of, and which will be correctly indexed by Spotlight):
tesseract image.png output-file -l eng pdf
The second output-file argument there is the path and filename of the output - note that I didn't include a .pdf extension because Tesseract adds that automatically - so the output will be in a file called output-file.pdf.
To get out just the plain text:
tesseract image.png output-file -l eng txt