I would be looking into "masking images in Photoshop with transitions"- you can have subtle transitions from the foreground image to the background image by "brushing into your mask" the transition areas. You are correct that a stark shape (rectangle or ellipse) outlining the foreground image, in this case, would not look so good.
As @Joonas said in the comments this would be easier done in Photoshop by masking your "food image" into your "background image".
This is done by placing your "food image" on a layer above your "background image" and then creating a mask on the "food image" layer- then simply use the brush tool with a soft edge brush to paint back the areas you want to show
This can also be done in Illustrator but is more complicated. I achieved the following results using an "Opacity Mask" rather than a "Clipping Mask"- (Please see this excellent answer from @Scott to explain the difference between the two)
How to edit clipping mask path after creating in illustrator?
I used a "free form gradient" to create the mask in the transparency panel- again, for this situation, this is a much easier task to perform in Photoshop