Solid state quantum emitters are a prime candidate in distributed quantum technologies since they inherently provide a spin-photon interface. An ongoing challenge in the field, however, is the low photon extraction due to the high refractive index of typical host materials. This challenge can be overcome using photonic structures. Here, we report the integration of V2 centers in a cavity-based optical antenna. The structure consists of a silver-coated, 135 nm-thin 4H-SiC membrane functioning as a planar cavity with a broadband resonance yielding a theoretical photon collection enhancement factor of similar to 34. The planar geometry allows us to identify over 20 single V2 centers at room temperature with a mean (maximum) count rate enhancement factor of 9 (15). Moreover, we observe 10 V2 centers with a mean absorption line width below 80 MHz at cryogenic temperatures. These results demonstrate a photon collection enhancement that is robust to the lateral emitter position.