One of my favorite Windows features is the ability to slam a program into the side of the screen to auto-resize it to fill that half of the screen.
Is there any program I can download for Mac that makes this feature available on macOS?
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Have a look at BetterSnapTool on the App Store:
BetterSnapTool allows you to easily manage your window positions and sizes by either dragging them to one of the screen's corners or to the top, left or right side of the screen. This enables you to easily maximize your windows, position them side by side or even resize them to quarters of the screen.
I had a client show this to me and they seemed pretty pleased with it. It also has a rating of 5 stars with 3500+ reviews. I personally don't use it (no need) but from the looks of it, it appears to be a good solution.