I had seen two Hampton Bay Grayton II which had a low speed capacitor completely dead. Grayton (at least ones made by PowerMax) has a dual capacitor. One capacitor for low and other for medium and both are used for high.
In my old house I had 2 Cheshire’s, one the color yours is and a plain white on, then I had a unknown outdoor fan on my back porch that didn’t work…then in the other 2 rooms I had 42” SMC’s then in the living room a 52” unknown hugger.
4:21 either it wobbles that way because of a loose ceiling fan box, or, the ceiling fan mounting bracket is just loose, so since you think that's not safe, you can just take the canopy down and tighten the bracket, or check if it's the ceiling fan box itself.
@@TPNWR10 the fan still vibrates while on low, so it’s trying to spin but it can’t, I think it’s a bad capacitor. Someone else’s video an a grayton just like this one has a bad capacitor and low doesn’t work on theirs either