Since the seamlessClone method is not available in the officially distributed opencv.js builds, I attempted to build my own opencv.js module by following the steps mentioned here.
I added 'seamlessClone' to the photo section in the opencv_js.config.py file and was able to build it successfully. The seamlessClone method is available in the browser but if I try to use it, I get an error "6607080" without any other information. I'm not sure I've added everything right to get seamlessClone working.
Edit (19 November 2021):
Alright so I tweaked the coordinates of the center point a bit, from (50, 50) to (215, 63), the final command being:
cv.seamlessClone(source, target, mask, new cv.Point(215, 63), dest, cv.NORMAL_CLONE)
This is at least not throwing any errors, but the output is still not as expected. I've added the images in detail in a comment on this github issue.