Negative feedback from block diagram to circuit components
The resistor RE provides (output)-current-controlled voltage feedback. Therefore, for analyzing the feedback mechanism, it is correct to consider the BJT as a transconductance device with voltage-in and current-out.
From this consideration we already can conclude that the feedback factor will be a resistive quantity.
Applying the transconductance view it is a simple matter to write down the output-to-input ratio ic/vbe with vb=vs and ve=icRE. (Note: All the variables are differential values; for simplicity I have assumed ic=ie with ib=0).
From this, you can find the closed-loop &quot;gain&quot; ic/vs (closed-loop transconductance). Now - analyzing the denominator of this ratio, you can find the loop gain expression and the feedback &quot;factor&quot; (which has the unit &quot;ohm&quot;). Of course, the numerator is identical to the open-loop &quot;gain&quot; (open-loop transconductance).