How to extrude as a round shape in concentrated areas? I hope that I'm explaining my question right as I'm new to blender but I really am at a loss here. I've been stuck for a couple days now of what to do with this.

So, I'm trying to make a side table, this one specifically: here. Everything was going good until I came to the point where I needed to extract round shapes (sorry, I don't know how to explain this), which I've watched many tutorials and thought I could do it also, but I couldn't. I've added more loop cuts, did the bevel action (which created a totally weird shape in diff directions), etc. Either I'm doing those things wrong (possibly since I'm new) or I just have to re-do what I did to make it so I can do these actions correctly.

Let me show you some photos to help explain what I mean (top is what my whole thing looks like, bottom w/paint done on it to show what I need it look like):





So in the first photo I did bevel it because I thought that was what could help me make it round but I could only do the sides of each face to get it round. I have had no idea how to do make the whole thing extend round. I also have no idea how to then make all of them the same size etc so I ran into that as well.

I'm sorry if this makes no sense. I have no idea how to correctly term things but I hope someone could help me or point me in the right direction on how to do this.
Here's how I would go about it.

lets say we have our initial shape (mine is slightly different):



I extrude a rectangle out of each one (Alt + E , extrude along normals):



Now, I select only the long edges (this can be done quickly using the box select in x-ray):



Then, I just bevel the edges to create a circle:



Final Result:



If you want yours to be more circular, just extrude out a larger square initially.