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Although I can’t help you with your question per se (and it’s been over six months without anyone else answering), I thought I’d let you know how I solved my similar problem.
I too wanted an OCR function in a chrome extension and started digging into tesseract to begin with. When I couldn’t solve it I moved on and instead used OCRAD.js and GOCR.js for my project. Although perhaps not quite as powerful as tesseract, I’m fully satisfied with my result.
Both OCRAD and GOCR are simple to include in your manifest.json and then you call the functions in your script by calling them as functions: OCRAD(image) or GOCR(image).
OCRAD has a nice demo page where you can test the functionality for your desired images before using it: https://antimatter15.com/ocrad.js/demo.html