Wobbling at low speeds

You might want to check out the information in this article:

https://www.2carpros.com/articles/steering-wheel-shakes-when-accelerating-or-braking

But this sounds like a broken belt in a tire, usually a rear one. The dandy clue you included is the low speed at which this occurs. Finding the bad tire is probably going to require an inspection at a tire and alignment shop. When you feel the thumping at higher speeds, you will find a raised area around the tread, like if the tire has a tumor. That would be the left tire in my nifty drawing. If that gets really bad, you will see the tread squirm left and right as you spin the tire.

What is harder to find is the broken belt that occurs so slowly, the raised tread wears down from normal driving. This can go on for months before you finally start to notice the subtle left and right movement. With a bad rear tire, you will feel the seat or the whole car move sideways a little. If it is a bad front tire, you will see the steering wheel oscillate back and forth once per tire revolution. This type of defect is a lot harder to diagnose. When spinning the tire, the portion of tread that hits the road looks fine, with no squirming or tumor. That tumor did form, but it wore down. You have to look deeper into the grooves and watch for a spot on the carcass that moves up and down as you spin the tire. That would be the red highlighted area at the bottom right of the right tire in my drawing.

During the inspection, the mechanic will also check the ball joints and tire rod ends. At the mileage you listed, expect to find parts that are worn. He will also "read" the tire wear patterns that point to those worn parts, and/or alignment problems.