This is a great addition.

Most basic answer I personally would do. Remover the vent from the wall (cut the tape at the joint and remove the slip joint) Cut a rectangle of dry wall out that goes above the bad patch and below the current pipe. (Drywall saw or razor knife)

If possible cut your piece out on both sides until you hit studs. Then, aim for your cut to land in the middle of the stud so you can screw the new piece into the studs.

Use the cut-out piece of drywall as a template to mark a replacment piece of drywall and cut out.

Remove and foam that might hit the new piece of drywall using a drywall knife, razor, cheap bread knife ext.

Using a hole saw, razor knife, drywall saw, jig saw or whatever, you have to cut the new hole for the vent pipe. (Again using the cut out drywall as a template for where to put the hole.)

Put new piece back up on the wall. (Test fit you pipe at this point to make sure you have the hole in the correct spot)

Screw in, mud, spray texture the replacment piece in place. (Lots of youtube videos on this)

Re connect vent pipe. And retape seam. Or paint first.

That should be it.

You could also do a quick repair which would be. Try and get the top circle patch as flush to the outside drywall as possible. Clean out the foam that sticks out past the front edge of drywall. Buy premixed drywall putty in a medium size tub and texture spray in a can. Fill all the voids with putty and make the finish as smooth as possible. (This might take a few layers depending on how deep you have to fill) Apply texture spray on top. Paint. Won't be stunning, but it will better then what you have.

Hopefully this gets you headed in the right direction.