Having grown up hunting Wyoming mulies, you won’t find me without a spotting scope even out in the sage brush, so I’d suggest an entry level spotting scope rather than new binoculars (although you will quickly see the value of clear optics).
The reason you’ll see more bucks with the help of a spotting scope is that a bedded down deer will stand up to stretch at mid day and that’s when carefully looking at draws will pay off. You also might see antler tips just sticking up with the body completely hidden. With only binoculars you’re missing half the deer within a mile of you.
I look over an entire area with binoculars then pick apart draws and any small ridges or bumps in elevation - some deer want to hide in draws and some like to be up a little bit to see, but still be behind vegetation.
I buy the young hunters in our family a used Windriver off eBay when come up for under $100. Not perfect - about like a new $300 scope, but much better than nothing. Then I’ll spend another $100 on a used Gitzo tripod off eBay - these are professional photography tripods that are rock solid. They come in a series from 0 to 5, with five being the largest - series 2 for carry, sizes 3-5 for car use. With $200 in gear, in the wind you’ll see as well as a new $3000 scope on top of a flimsy new $100 tripod - that happened in Yellowstone last summer.
Get a big ball or fluid head - or make a simple swivel out of heavy aluminum and a couple of bolts - we’re not curing cancer.
I used to say don’t waste money on binocular tripod mounts and just rest the binoculars on the spotting scope turned sideways, but that’s just the way I hunt - look all around you, not just forward - after a binocular scan, pick apart the same country with the scope. I’m not sure how that’s possible with a binocular mount - mounting and dismounting 50 times a day isn’t realistic, so you’ll avoid picking apart things with the scope.