Let $X=(x_1,\ldots,x_n)\in\mathbb R^{p\times n}$ have independent real columns with finite second moments, not necessarily centered or identically distributed. For $z\in\mathbb C\setminus[0,\infty)$, we compare \[ G^z=\left(\frac1nXX^\top-zI_p\right)^{-1} \] with a deterministic matrix $\tilde G^z$ defined by the second-moment profile $(Σ_i)_{i\in[n]}$, where $Σ_i=\mathbb E[x_ix_i^\top]$. We prove finite-dimensional $L^q$ bounds for $\text{tr}(A(G^z-\tilde G^z))$ in terms of moments of centered quadratic forms, without assuming independence among the coordinates of a column. Operator-test bounds impose no trace-growth or aspect-ratio restriction and display explicitly the effect of the sizes and repetitions of the second-moment matrices $(Σ_i)_{i\in[n]}$. Under $\sqrt p\sup_{i\in[n]}|Σ_i|_{\text{HS}}=O(n)$, Hilbert--Schmidt-test bounds allow the heterogeneity of the profile to be controlled through approximation by commuting positive-semidefinite matrices. Additive deformations also yield deterministic equivalents for resolvent sandwiches. All bounds are locally uniform away from $[0,\infty)$.

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