From my experience, in chrome browsers, tap and hold context menu will differ in some cases (I’m not exactly sure depending on what), but sometimes you will have the option copy link address which will copy just the image link, and in other cases you will only have share image option which I personally never use.
It seems like share image option copies the image into the clipboard and if you choose to include the link, it will also paste the link bellow (link to the page where you copied the image from, and not the direct link to the image, it seems like). And that will work (including the link) only if you share the image to a specific app. If you choose copy image option from the share menu, it will only copy the image to clipboard without the link, even if you choose to include the link as well.
So in such cases you would have to long tap on the image, open image in new tab and then copy the link from the url bar, which is how I always done it, but it is pretty stupid that you can’t copy only the link from that share menu.
Maybe there is some other way that I don’t know of ¯*(ツ)*/¯
In firefox browser you will always have the option to copy image location, which will copy just the image link, I’m not sure about other browsers.