Yes, MPNs, including ET, can cause both dizziness and vertigo. There can be several mechanisms via which ET can cause balance problems and other neurological issues. One would be microvascular occlusion (microthrombi blocking very small blood vessels), another one would be inflammation that is typical to MPNs.
Some people are helped by antiplatelet therapy (e.g., aspirin), although this seems to solve these issues completely only in a third of people.

If you want to make sure this is from ET and not from another health issue, it is better to see an ENT specialist and have investigations there to exclude inner ear problems. I have both dizziness and vertigo and I had a full investigation at ENT that excluded typical inner ear issues but showed I am doing my balance almost exclusively using my vision. The specialist thinks it is because microthrombi affect the functioning of my inner ear, that my body switched to using the eyes far more for balance.
In my case, aspirin helps with tingling and numbness, but does nothing for dizziness and vertigo. For that I have other strategies.

Hope you get help with this issue.

I'm not sure if it is vertigo or not, but I find I do get a slight bit of dizziness from time to time. I would be interested to know what actually causes the dizziness. A friend who actually had vertigo said after taking vitamin k it cleared up for him. But he doesn't have ET and I'm unsure if vitamin k is safe to take for ET patients.

I do not know about ET, but I have PV and have experienced vertigo.