Is that a second connected plate in front of your finger like the one pinched by your thumb and finger? I think I've seen that kind years ago. And is that a bolt/post on the front side of the right part at the 1" arrow?
You might continue to have a problem finding them. Scour the search engines and then you may want to replace them all at some point if you can't find them.
Not seeing more angles makes it a bit difficult to tell exactly what it looks like to do my own search.

Good luck with it. Maybe somebody else on here will recognize it right away and know where there are some.

Why do you need to replace them? If it is only for
cosmetic reasons, then you can refinish them, or have
them professionally re-plated.

It is probably a proprietary hinge design made for a particular manufacturer. Crown Point uses something similar (with a threaded plate that fits into a routed notch to allow adjustment) but it doesn't have the half-inset, lipped feature I seem to be seeing here.
It may end up with you buying hinges with a similar door/cabinet relationship with a conventional mounting (screws).
Casey

There are plastic-like pieces that are broken and most of these hinges now sag, so it is not for cosmetic purposes.

yes, that second piece is connected. the bolt/screw goes into the back of the cabinet door.