Sounds like at least one of the wheels might be out-of-round on one or both sides.
You should put all 4 on a Hunter Road Force Balancer. Been there, done that too much with current wheels and tires.
Also, despite what the optimistic "green/ok" road force measurement says on HRFB, get the actual road force in lbs for each wheel from the tire tech. The HRFB will "green" anything under like 20lbs. But believe me, I've been through a lot and I can feel/hear about 5lbs road force, so anything higher than that chances are you will too. I think the 20lbs or less number is for people that are either oblivious or maybe on large sidewall cars or SUVs it's less noticeable. On my S5, it's audible though it produces no real shake anywhere.
The fact that you get a vibration in the steering wheel seems to indicate a front tire. Start there, aim for under 5lbs road force. If the tire is way out of whack, loosen it on the rim and reposition it as that often helps a surprising amount. Worst case, a tire or rim is out of round and cannot be fixed. The HRFB has a tool like a record player arm that can be sat on the rim bead while it spins that can measure roundness/runout.
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