Need to Fix Broken Edge Loop? I'm trying to create a nightstand that has these inset circular handles. See below:





However on the bottom drawer handle, the edge loop of the circle is broken in two halves so I can't use the extrude/inset face tool to create the same look as the top one. See what I mean here:



I've tried to Merge Vertices, I've tried to Connect Vertices, I've tried Make Edge/Face. Usually I can just bungle my way through something stupid like this but I'm stuck and can't seem to google it either everyone's situation seems different. Which makes me think I'm missing something really dumb and simple. My brain doesn't seem to work with simple I over complicate. Anyway any ideas? Much appreciated in advance thanks.

Editing to add my .blend file.
An alternative, Sub-D approach: absolutely no better than yours, but with all the tools in Blender that are geared to working this way, personally I find this kind of pattern  gives rise  to fewer mysterious faults in the mesh, and is easier to tweak later.



Starting with a bevelled pair of drawers:


CtrlR  Cut in 3 edge-loops in both directions
F Fill the central faces
AltP Poke the filled faces
CtrlShiftB bevel the central vertices
Select both resulting faces, and Loop-Tools > Circle, ( or Space-Bar > Circle) setting the Radius field as desired.
Inset I and Extrude E the circular faces, to create holding loops and the recess.
Assign a Subdivision Surface modifier.