For anything GPU-rendered, applying a rotation matrix to a texture sample and/or frame-buffer write is trivially cheap (see also why Vulkan prerotation exists on Android). Even ignoring GPU-rendering, you always are doing a copy as part of rendering and often have some sort of matrix operation anyway at which point concatenating a rotation matrix often doesn't change much of anything.

Pretty much every pixel rendered these days was generated by a shader so gpu side you probably already have way more translation options than just a 90° rotation (likely already being used for a rotation of 0°). You'd likely have to write more code cpu side to handle the case of tell the gpu to rotate this please and handle the UI layout diffrence. Honestly not a lot of code.