If you want to store exactly the same cover, please don't use the clipboard functions. The image in the clipboard is stored as DIB (Device Independent Bitmap) and Mp3tag creates a JPG from this while pasting.
Please get a better jpeg encoder. 90% of online bmp-to-jpg converters can achieve much smaller file sizes without any quality losses. EDIT: Yeah, it turns out I was wrong about that and there are very minor quality changes, at least in the ones that approach the original file size, except for Irfanview.
Edit: I just realized that another possible reason for the high file size could be bitmap rendering. For example if you copy an image like https://i.imgur.com/4MSj5Bt.jpg and use something like PasteIntoFile or PasteasFile to save it as a bitmap file, you'll get a bmp file of 4.57 MB, but if you paste it into GIMP or Irfanview, then export it, you'll get a bmp file of 3.43 MB.
If you download these images to a local folder first, do they have the same image details as what you expected from Chrome? And if you then copy and insert these local files to mp3tag do they still change, or maintain those same local file stats? I don't think I would necessarily trust the image size info provided by a web browser to be exact compared to the actual file info.
From my first comment it is clear that I have already compared file sizes of clipboard images (bmp files) and source file images (jpegs). Besides, I never said I was looking at the file size info on Chrome (which, like you said, isn't something that's easily or accurately done).
Anyways, I have already acknowledged that except for Irfanview, all those other jpeg converters are not 100% lossless so I don't have a problem anymore...