Seems to me, the smallest possible everything bagel would be 100% bagel.

There are a couple possible interpretations of everything bagel. Either everything is on top of the bagel, or everything is between the two halves of the bagel. Or somewhere in between.

The latter extreme allows for the smallest everything bagel because anything that is between the two halves counts, while the stuff on top might be considered separate. For example, is another bagel on top a topping, or another bagel? Are the toppings on that bagel also toppings of the first bagel?

So the contents a bagel inside the first bagel are also contents of the first bagel, meaning that an everything bagel can then contain an everything bagel, which it must since an everything bagel is a thing , while only containing everything that isn't an everything bagel once.

Now, since the interior everything bagel must also contain an everything bagel, and this applies to THAT bagel, at a point, there are so many bagels that everything else is negligible.