Background: Chronic ulcers are a major healthcare challenge due to their prolonged course, recurrence, persistent microbial colonization, and impaired tissue repair. This study developed sodium alginate–collagen hydrogel dressings reinforced with cotton fabric and functionalized with green-synthesized copper oxide nanoparticles (CuO NPs) to combine exudate absorption with localized antibacterial activity. Methods: CuO NPs were synthesized using gallic acid and orange peel extract and evaluated for cytotoxicity and antibacterial activity against Staphylococcus aureus and Escherichia coli. Sodium alginate–collagen dressings containing different glycerin concentrations were assessed for swelling capacity, morphology, structural stability, and tensile performance. The formulation showing the best overall physicochemical and mechanical performance was selected for CuO NP functionalization and antibacterial evaluation by agar diffusion. Results: The selected 50GS-NPs-CuO formulation showed an IC50 of 79.9 µg/mL. At 70 µg/mL, CuO NPs produced significant time-dependent reductions in bacterial viability, reaching 96.6% for S. aureus and 91.44% for E. coli after 72 h. The dressing containing 2% sodium alginate, 0.5% collagen, and 2.5% glycerin exhibited the highest swelling capacity (476.82 ± 3.80%) and tensile strength (148.7 ± 5.5 N). CuO-functionalized dressings showed concentration-dependent antibacterial activity, with consistently greater inhibition against S. aureus than E. coli. Conclusions: The developed dressing integrates high fluid absorption, mechanical stability, and localized antibacterial activity, providing a promising platform for advanced chronic-wound management.