We revisit the extraction of the \(|V_{ud}|\) Cabibbo-Kobayashi-Maskawa (CKM) matrix element from the superallowed transition decay rate of \({}^{16m}\text{Al}\rightarrow {}^{26m}\text{Al}\), focusing on finite nuclear size effects. The decay rate dependence on the \({}^{26}\text{Al}\) charge radius is found to be four times higher than previously believed, necessitating precise determination. However, for a short-lived isotope of an odd \(Z\) element such as \({}^{26}\text{Al}\), radius extraction relies on challenging many-body atomic calculations. We performed the needed calculations, finding an excellent agreement with previous ones, which used a different methodology. This sets a new standard for the reliability of isotope shift factor calculations in many-electron systems. The \(\mathcal{F}t\) value obtained from our analysis is lower by \(2.2\sigma\) than the corresponding value in the previous critical survey, resulting in an increase in \(|V_{ud}|^2\) by \(0.9\sigma\). Adopting \(|V_{ud}|\) from this decay alone reduces the CKM unitarity deficit by one standard deviation, irrespective of the choice of \(|V_{us}|\).