resizing to 300dpi

[GeorgeMiller3]

I start with a 16x9 4767x2667 image.
In Image Size I change it from 72px to 300px and change the new size back to 4767x2667.
When I save the file jpg it reverts back to 72px.
I do the same sequence in Photoshop and the image stays 300px.
So either Pixelmator Pro or Photoshop are wrong?

Super Resolution increases the size (14301 × 8001 pixels) but not the resolution.
When I view Image Size it shows a new resolution of 216.
When I open the image with Preview it shows 72dpi.