Background: Apicoectomy remains a predictable treatment option for persistent apical periodontitis when nonsurgical retreatment is not feasible. While advances in endodontic microsurgery have improved periapical healing, the influence of flap design on soft-tissue outcomes and patient-centered parameters continues to be clinically relevant, particularly in esthetically sensitive regions. Materials and methods: A prospective clinical study was conducted on 90 patients requiring apicoectomy in maxillary anterior and premolar teeth. Patients were equally allocated into three groups based on flap design: IS (n = 30), PBI (n = 30), and OL (n = 30). All surgeries were performed using standardized microsurgical protocols, including ultrasonic root-end preparation and bioceramic root-end filling. The primary outcome assessment included postoperative gingival recession at 3 months. Secondary outcomes comprised interdental papilla height changes, postoperative pain and swelling, scar visibility, and radiographic healing at 12 months. Data were statistically analyzed using appropriate parametric and nonparametric tests with significance set at p < 0.05. Results: The IS demonstrated significantly greater gingival recession and papilla height loss compared to the other groups (p < 0.001). The gingival recession at 3 months was the predefined primary outcome. Measurements at 1 month were predefined secondary/exploratory time points intended to capture early trends in healing. The PBI group showed the most favorable soft-tissue outcomes, with minimal recession, superior papilla preservation, and lower postoperative pain scores. The Ochsenbein–Luebke (OL) flap exhibited limited gingival recession but a higher frequency of visible scarring. Radiographic healing at 12 months was high and comparable across all three groups, with no statistically significant differences. Conclusion: Flap design significantly influences soft-tissue healing and esthetic outcomes following apicoectomy. The PBI provides optimal gingival and papillary preservation in esthetically demanding regions, while the OL flap remains a useful alternative in selected cases. Radiographic success is not compromised by flap selection when modern microsurgical techniques are employed.