If it has a stem of any kind , it is not a puffball.
Now we got that out the way lets look at the pic.
I think it is a little on the small side for a giant puffball given the scale of the grass, but even puffballs the size of sheep must start small.
Confused by what you call "mushroomy" inside, if it is a giant puffball and you are going to eat it it should be white and uniform all the way through with only the skin being a bit tougher and leathery.
Janiepopps' comment about it being brown and powdery inside - sorry that just isn't right, they start white when fresh and edible, turn beige inside then on to green, then dry out and become very dark brown and powdery.
The puff in puffball is the brown powder spores that puff out when they are dry and mature and you happen to step on them.
I dont like ID ing fungi on the web because someone might take my advice and it could turn out to be wrong :yikes:
To put it bluntly there are way too many scare stories and conflicting opinions for it to be a good idea. Have a search for the great sorrel debate here if you like lol.
Having said that I love picking and eating wild mushrooms including puffballs.
My advice, get a book and a local expert to confirm,
If it is indeed a puffball , they dont taste much so go for something tasty to fry it in, bacon fat is good though vegetarians may prefer to add some seasoning to plain sunflower oil.
Hope that helps
Tant