AFAIK Vulkan doesn't natively support V-Sync, although there are some vendor extensions to it that add V-Sync support. I'm not sure if Dolphin uses those extensions or not, but it might be the cause, especially if you don't experience this issue on the other backends...
Avell A70 MOB: Core i7-11800H, GeForce RTX 3060, 16 GB DDR4-3200, Windows 11 (Insider Preview)
ASRock Z97M OC Formula: Pentium G3258, GeForce GT 440, 16 GB DDR3-1600, Windows 10 (22H2)
ASRock Z97M OC Formula: Pentium G3258, GeForce GT 440, 16 GB DDR3-1600, Windows 10 (22H2)