Organometallic half-sandwich complexes [(η5-Cp)IrCl(L)]PF6 (1) and [(η5-Cp)RhCl(L)]PF6 (2) were prepared using pentamethylcyclopentadienyl chloride dimers of iridium(III) or rhodium(III) with the 4-amino-N-(2,2'-bipyridin-5-yl)benzenesulfonamide ligand (L) and ammonium hexafluorophosphate. The crystal structures of L, 1, and 2 were analyzed in detail. The coordination reactions of the ligand with the central ions were confirmed using various spectroscopic techniques. Additionally, the interactions between sulfaligand, Ir(III), and Rh(III) complexes with carbonic anhydrase (CA), human serum albumin (HSA), and CT-DNA were investigated. The iridium(III) complex (1) did not show any antiproliferative properties against four different cancer cell lines, i.e., nonsmall cell lung cancer A549, colon cancer HCT-116, breast cancer MCF7, lymphoblastic leukemia Nalm-6, and a nonmalignant human embryonic kidney cell line HEK293, due to high binding affinity to GSH. The sulfonamide ligand (L) and rhodium(III) complex (2) were further studied. L showed competitive inhibition toward CA, while complexes 1 and 2, uncompetitive. All compounds interacted with HSA, causing a conformational change in the protein's α-helical structure, suggesting the induction of a more open conformation in HSA, reducing its biological activity. Both L and 2 were found to induce cell death through a caspase-dependent pathway. These findings position L and 2 as potential starting compounds for pharmaceutical, therapeutic, or medicinal research.