Paste image from the clipboard into a PDF in Preview
You CAN do it. At least this is what worked for me on MacOS Catalina and Preview Version 11.

Copy onto the Clipboard, the image that you want to paste on your PDF page.
Go to Preview -&gt; File -&gt; New from Clipboard.
This will basically create a new Preview document with your image in it. Now click anywhere on the image, press Cmd+A to select the entire image, press Cmd+C to copy and then (this is the crucial part!!) press Delete to delete the image.
You will see a blank screen in Preview since you have deleted the image. Press Cmd+V and your image will reappear, but now, in a different format that can be copy-pasted across Preview documents.
Finally, select this 'new format' image using Cmd+A, copy it using Cmd+C and navigate to your PDF document and paste using Cmd+V.

Voila! You can paste the image anywhere in your PDF document and on any page and you can resize and edit it just like you can with shapes. I think Apple didn't intend this to happen and I hope they don't read this and change this feature :P