how would you make the selected object convex so it fits smoothly around the other object?
I can’t figure out what you want here. Which part would it fit around so it becomes convex? Can you do a quick line drawing in paint or something?
im talking about the whole selected part outlined in orange. so it has a nice transition from the bottom to top
Yeah like that, without artifacts ofc. What are the ways to do it?
There are no artifacts there, those are sharp corners 
That’s just Bevel with a few segments. If you really need it as a separate object, you can duplicate the four faces, separate them into their own object, bevel the corner, delete unwanted faces, extrude the ends and cap the holes.
i tried it with beveling with a few edges selected but it wasn’t turning out properly. Thank you tho, I’ll try that some more
Oh man, thank you! Appreciate this a lot!