Is it possible to bake in perspective projection?

For some reason I need to get an image of uv representation in the 3d world from the camera view. This can be simply done with just a regular camera rendering and Texture Coordinate node. And its great. But it doesn’t have the ‘margin’ option as in the bake panel (I need these border extensions in the final image).
So I tried to bake then. I just fitted a plane from the camera view to the target direction. But the baking always happens with orthographic projection but I need exactly the same result as regular rendering.

First image from a camera view, second is the baking. Do not care for different colors - the projections are DIFFERENT. Is it possible to bake as in the camera view projection?

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