= Solution
On $N=\mu^{-1}(-1/4)$, the diagonal <fundamental vector field> $X$ is nonzero, since the <fixed-point set> lies at <moment map> values $0$ and $-1/2$. The <nondegenerate bilinear form> $\omega_p$ and $d\mu=\iota_X\omega$ imply $d\mu\ne0$, so $-1/4$ is a <regular value>. By the <regular level set theorem>, $N$ is a three-dimensional <embedded submanifold> of the four-dimensional <Complex projective plane>.
At $p\in N$, set $W=T_pN=\ker d\mu_p$. Then $\omega(X,v)=0$ for every $v\in W$, so $X\in W^\omega$, the <symplectic orthogonal complement>. This complement is one-dimensional and $d\mu(X)=\omega(X,X)=0$, giving
$$
\boxed{(T_pN)^\omega=\mathbb RX_p\subset T_pN.}
$$
Thus \b[the level set is a <coisotropic submanifold>, neither an <isotropic submanifold> nor a <Lagrangian submanifold>]. Indeed an <isotropic subspace of a symplectic vector space> in dimension four has dimension at most two, whereas $\dim N=3$. Its <characteristic line field> is generated by the diagonal <circle> action.
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