Child taking up TW citizenship 入籍


My wife is Taiwanese and our baby girl currently holds a US passport. We are visiting Taiwan soon under a 60 day visitor visa . During our time there we intend to register our baby as a Taiwan citizen with household registration i.e. enter on a US passport, complete quarantine, register with TW immigration & household registration. My wife and baby will be in Taiwan for a longer time (90 days). Given the 60 days visa valid period, assuming household registration 入籍 process is completed within this period, would my baby be considered as ‘overstaying’ given that she the visa is only for 60 days?

The above scenario is quite common and I understand when a newly registered national leaves TW, the Immigration counter only stamps in the Taiwan passport and not the home country passport.