Background/Objectives: Seasonal influenza threatens global public health through rapid mutations. This study evaluated the prevalence and molecular-genetic characteristics of seasonal influenza viruses circulating in Kazakhstan during the 2023–2026 epidemic seasons. Methods: Nasopharyngeal swabs (n = 1756) and serum samples (n = 718) were screened using RT-qPCR, HI, and ELISA assays. Selected A(H1N1)pdm09 isolates underwent full-length HA and NA gene next-generation sequencing, followed by phylogenetic and phenotypic analyses. Results: Influenza A(H3N2) strains dominated in Kazakhstan during the 2023–2024 and 2025–2026 seasons. Conversely, the 2024–2025 season showed a shifting landscape, characterized by co-circulation of influenza B and A(H1N1)pdm09 strains belonging to genetic clade 6B.1A.5a.2a (subclades C.1.9 and C.1.9.3). Mutational mapping revealed ongoing in situ microevolution adjacent to the receptor-binding site (HA-R222K). Genomic screening of the NA gene identified critical I223R and S247N mutations traditionally linked to resistance. In silico profiling predicted that while the majority maintained baseline sensitivity, the solitary A/Shymkent/NRL-1999/2024 isolate harboring the I223R substitution exhibited a multidrug-resistant genotype to oseltamivir, peramivir, and zanamivir. Conclusions: These findings demonstrate dynamic inter-seasonal etiological shifts and the predicted emergence of an independent resistant lineage (NA-I223R). This underscores the necessity for continuous, expanded genomic surveillance of respiratory pathogens across Kazakhstan.