Terrible resolution when transforming image. NOT RESIZING IT. I AM NOT MAKING IT BIGGER

Moderator please change the label of this thread to macOS and Windows (and delete my post).

Check the Interpolation setting in the Transform upper toolbar shown below. Try Bicubic Automatic or just Bicubic. If set to Nearest Neighbor you will see stair-step pixelation.

Yes, that's how it works when you're using rasterized images. There's no solution or workaround other than switching to vector graphics.

If you want to rotate and scale freely a pixel/raster layer, I would turn it into a smart object first.

Photoshop will still have to resample the image to render it, but it will keep the original pixels, so you can play with the transform freely without quality degrading.

Either way, you're better off starting with a higher resolution image than the final pixel size.

In extreme cases where I have to use some low res clipart, what I do is convert it into a smart object, and then open the smart object and upscale it by 200% with preserve detail 2.0 enabled, giving me a "good enough" image. Save, come back to the original, and play with the transform freely. Not perfect, but better than nothing.

Could you please post meaningful screenshots with the pertinent Panels (Toolbar, Layers, Options Bar, …) visible from the Transformation process? 

Smart Objects? 

What is the Photoshop > Preferences > General > Image Interpolation setting? 

What kind of image is it? Pixels or a shape? A shape should not be affected by rotation, or by shrinking or enlarging. A pixel image will be affected because the pixels need to be resampled. And yes, if you enlarge a part of a pixel image, that is the same as resizing that part. You make it bigger, so Photoshop has to ‘invent’ extra pixels to do that. Resolution (in ppi) has nothing to do with it.