The main issue here is that you are trying to use the oh-slider-cell. The cells are pre-styled containers that are very difficult to override and work with. They are really intended as the most “low code” option of just add it to a page and don’t worry about it. If you really want the look of the extra container you can try to use an oh-slider-card instead which gives you many more options for styling the card container itself, but the best choice is just to use the oh-slider directly. This will match the style of your buttons more closely.
Whichever option you choose, styling the slider itself is a little tricky. This is actually covered explicitly in the advanced widget tutorial where a vertical slider it fit into place in a larger widget: