I have a suntour linkage spring suspension post on my ebike. I find it essential for going faster than 20km/h.

The biggest factor for an ebike is your motor assist level. Basically, the less force you apply to the pedals, the less bob you get, and more of your body weight is on supported by the saddle.

Having said that, a suspension post will change your bike geometry. A linkage post will slack back a bit when you sit on the saddle, which would be a problem if you already have your saddle slammed all the way to the front.

Anyway, I do agree that you should start with changing to bigger tyres

could you elaborate on that a bit?