Convert psd file to, or edit psd files with .ai or .indd

You can place the PSD in an Illustrator document or an InDesign document using File > Place.  In the options, make sure that the Link check box is disabled (this will make your resulting file larger, but will keep it self-contained).  Then save the AI or INDD as you would normally.

If it's a photo, you're already in the best application for editing it.

Photoshop is a pixel editor not a vector or editor like AI.  While some Pixel images can be converted to a vector image not all pixel  images can be converted to vector graphics. There would be too many complex Vector Paths layer's  to be practical.   Most likely exceed the  layer limit AI would have. Here is is a image I found on the web I converted to a not so bad vector image not  multiple colored or even 256  tones of gray.  Note the number of control points in the single layer vector path.  Which does not do justice to the original pixel image.  Imagine if you needed to handle 16 million colors a pixel image may have.