Why is strontium(II) ion bigger than krypton atom?
Sr2+ is exactly the same as Kr, in terms of electrons and orbitals.

I think the appropriate word for this relation is isoelectronic.
According to Ptable and LumenLearning, $\ce{Kr}$ has an atomic radius of 88 pm, while $\ce{Sr^2+}$ has an atomic radius of 132 pm. Although it is true that $\ce{Kr}$ and $\ce{Sr^2+}$ have the same electron orbital configuration and $\ce{Sr^2+}$ has two more protons than $\ce{Kr}$, $\ce{Sr^2+}$'s greater nuclear attraction is likely countered by the nature of metal ions being more willingly to lose electrons, which implies the electrons are more loosely held by the nucleus than the noble gas $\ce{Kr}$.
Another reason I conjecture is that $\ce{Sr^2+}$ has unfilled 5s orbitals to readily accept promoted electrons, while $\ce{Kr}$'s electrons have less tendency to fill the 5s orbitals because the property of being a noble gas.