From what I have seen so far the quality of the image on the TV behind the mirror once turned on is not acceptable. Not saying they have not improved, but with as great as TV's are today, I'm not willing to sacrifice the image. Maybe consider a wall cabinet to conceal the TV instead.

@bananamamma - if you save the photo of the item you’re searching for as a screenshot and then (using Google Photo) go to that photo, you click/touch the little icon (dot with broken square box around it) that I’ve circled in the photo below. It will find other photos like it on the net. I think it’s called Google Lens.

I would call a glass/mirror company and ask. I suspect they do have something strong enough to adhere it, but the likelihood of it not damaging the mirror behind might be very low. Like if they use an epoxy, you might not ever be able to get them apart, or if you do, the epoxy might be difficult to remove from the larger mirror.

Well, I am trying to make similar decisions on this myself. I too had come across that it is better to have sink lighting from the side rather than above but have found the layout to be challenging and busy. So, I checked houses for sale with 2500 - 3500 square feet and none of them had side sconces around their mirrors. And only one or two had frames around their bathroom mirrors. Most of them had one large mirror across the sink area with lights over it. A bathroom can be a busy area, so from a minimalist standpoint, no frame. Now a mirror in the Livingroom really needs a frame.