Need help identifying hinge for older inset cabinet door

[Cameron Richard]

I’m replacing hinges on an older cabinet and ran into a weird setup I can’t match at Home Depot/Lowe’s. The cabinet frame has a beveled/slanted inner edge, so standard wrap or partial wrap inset hinges don’t sit flat. The original hinge mounted inside without wrapping around that angled section.

I’ve attached photos of the frame and door. I’m just looking for the correct hinge type/name so I can search and order the right hardware. Has anyone run into this style before or know what hinge I should be looking for?

Thanks in advance.