In this work, we present new phenomenological extractions of the nucleon charge and magnetic radii based on its Dirac and Pauli flavor-separated $F_{(1,2)}^{(u,d)}\left(Q^2\right)$ form factors, over the extended range 0.0155 $<Q^2<$ 1.00 ${\mathrm{GeV}}^2$. Building upon the framework introduced by M. A. Albloushi et al. [Phys. Rev. C 109, 065201 (2024)] for the charge sector, the present study extends the analysis to include the magnetic radii, expands the fit procedure to ten overlapping $Q^2$ ranges, and employs a correlation-aware Generalized Least Squares (GLS) framework to quantify inter-range correlations. Both two-photon-exchange (TPE) corrected and uncorrected datasets are analyzed, and the impact of including or neglecting TPE corrections on the extracted radii is systematically investigated. In the TPE-corrected GLS analysis we obtain ${\langle r_p\rangle }_E=0.8478\pm 0.{0015}_{\text{(stat.)}}\pm 0.{0034}_{\text{(sys.)}}$ fm, ${\langle r_n^2\rangle }_E=-0.0885\pm 0.{0018}_{\text{(stat.)}}\pm 0.{0019}_{\text{(sys.)}}$ ${\mathrm{fm}}^2$, ${\langle r_p\rangle }_M=0.8468\pm 0.{0008}_{\text{(stat.)}}\pm 0.{0139}_{\text{(sys.)}}$ fm, and ${\langle r_n\rangle }_M=0.8935\pm 0.{0011}_{\text{(stat.)}}\pm 0.{0300}_{\text{(sys.)}}$ fm. The proton charge radius agrees with the ultrahigh precise muonic hydrogen ($\mu \mathrm{H}$) Lamb shift and PRad-I results and is smaller than the Mainz A1 extraction, while the neutron charge radius is below in magnitude the value obtained by the recent precise measurements of the neutron $G_E^n\left(Q^2\right)$ form factor at low $Q^2$ utilizing the connection between the $N\to \mathrm{\Delta }$ quadrupole transitions and $G_E^n\left(Q^2\right)$. The magnetic radii are compatible with global dispersion, lattice-QCD constrained, and TPE-aware analyses, with ${\langle r_p\rangle }_M$ and ${\langle r_n\rangle }_M$ differing by $\approx$ 5%, in accord with SU(6) spin-flavor symmetry expectations. These findings demonstrate that implementing TPE corrections within a correlation-aware GLS framework yields a statistically robust, phenomenological description of the nucleon's electromagnetic structure.

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• Elastic scattering reactions
• Nuclear radii
• Form factors