Is it normal that I can't use perspective/warp/cage/liquify transform on vector shapes?

I can apply normal transformation though. So I’m just curious.

For Warp, Cage and Liquify, there is no equivalent vector operation or representation. Liquify especially has the obvious effect of moving pixels around, which is not a ‘vector thing’.
Perspective sounds like and looks like it should be ok on vectors but it acts continously over a plane and stretches pixels making parts of a line thicker than other parts of the same line. Again, this is not a vector thing.
If you want some kind of perspective change effect on a vector object then you just need to drag the nodes around until you get what you want to see.
Maybe this needs a warning note to pop up saying “you can’t use this on a vector layer”?

You can put a transform mask on a vector layer and do this to get a permanent on-screen representatiom of the transform and it acts on the raster projection of the vector object. That may be a way around it if you really want to show these transforms on a vector object while keeping them as vectors.

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The best way I think, to present this in the application is just disabling Transform Tool on vector layer. Since it’s already possible to apply transformation via transform mask and Select Shapes Tool it causes confusion.

(*note) - After applying transform mask, you need to move vector shapes with Move Tool and not the Select Shapes Tool, otherwise the ‘transformed area’ will mismatch with where the original shape is.

But you can transform using the Free Transform. Maybe other modes could be greyed out though?