BG5GGC The resonant frequency of the antenna generally remains constant regardless of power level. If you notice a change, it's likely due to either: (1) the antenna not being properly fixed or (2) the antenna having poor quality.
NanoVNA cannot be used for online testing. If you insist on doing so, you will need to purchase a power meter or VSWR meter, but it is really not necessary. Instead, borrow one or use your NanoVNA to measure. In amateur radio scenarios, after using the NanoVNA for offline measurements, connecting it to the radio station for online testing is also essentially the same.