I agree that each eye most certainly had a stone in it. From the link you provided in thinking the stone closely matches the one on the right side all the way at the bottom.
The measurements are {Handle Length=33 1/2″ Axe Head Width=6″ Axe Head Height=51/4″}
I cannot imagine this being a kitchen tool. But now that you mention it I completely agree that it very well could be for a woman.
One photo shows where the axe made what seems to be very hard contact with something. Also attached is the backside of the axe head.

https://www.debarnsteenspecialist.nl/en/minerals/tumble-stones/swedish-blue-slag/

Mmm,, is this axe/hatchet by any chance on the small side compared to what a man would use ?? It just confounds me that what I am seeing looks more geared to a woman than a man !! Even the rotating pick looks feminine !! Kitchen tools have been the curved shape for hundreds of years !! And like I said,, the lovebirds and the flowers just are not what you would think of a man using as a tool !!
Look above and see if thats what your one stone may be !! I am sure there was one in each eye when made !!

Photos

I have attached now photos. The stamp on the bottom is difficult to read but it reads ” B.A Hjorth & Co. Stockholm Sweden”
Also included the piece on the top of the as axe head that swivels to add what I can only think is another function for a weapon. Also some better images of the painted handle.
Once again I cannot thank you enough for your input and time.

You didn`t say how the name was printed on the handle !! That can help with age of the axe !! Hjorth didn`t start making tools until 1896 !! He changed how the company name was used at some time to ABHCO !! Thats what I wanted to check !!