Recently, the generalized half-normal distribution with decreasing, increasing, and bathtub hazard function shapes was proposed, making it a more applicable, reliable, and flexible lifespan model. The task of estimating the unknown parameters and reliability features of the generalized half-normal distribution is looked at using adaptive progressively type-II hybrid censored data. The maximum likelihood and Bayesian estimation methods are both considered for this purpose. Two approximated confidence intervals, Bayes and highest posterior density intervals, are acquired for the various parameters. The Bayes estimates are obtained based on symmetric and asymmetric loss functions under the assumption of independent gamma priors. The Markov chain Monte Carlo approach is used to compute Bayes estimates as well as the various Bayes intervals. Monte Carlo experiments are used for assessing the efficiency of the various approaches. Finally, analysis is performed on two actual-life engineering datasets.