Most of the automatic humidor controls I’ve seen are only listed as having accuracy of +/- 3% RH or higher. Even with an accurate hygrometer, unless you’ve got a really nice well seasoned unit with temp control and are extremely careful about placement of everything that impacts airflow you’re going to have RH variations of several % RH throughout the humidor, particularly between the top and the bottom. This issue gets worse the taller your cabinet is. I guess the point I’m making is I’m not sure a sensor with +/- 1% RH accuracy is really necessary.
They can run on batteries as well, either as power backup or as primary power. FWIW the accuracy of the sensor it uses is +/- 1°C, 3% RH, and 1hPa.
Another option could be the Aqara temp/humidity sensors. They claim accuracy of +/-0.3°C and 3% RH, and are cheap/small enough that you could put several in your humidor to see the variation and trigger actions based on averages/mins/maxes. They can be a bit finicky to pair though, and don’t work well with many (most) zigbee repeaters.
Also keep in mind that the reported accuracy is the absolute accuracy, the effective accuracy once calibrated will be much better in most cases, particularly for something like this where you’re not dealing with extreme temperatures or large variations in either temperature or humidity.