What is this RC local feedback configuration?
It doesn't match any op amp amplifier circuits I've seen

In contrary, it is one of the well-known controller types applied in control systems: Proportional-Integral-Controller (PI). Here is the transfer function:

$$H(s)=-\frac{R_2+\frac{1}{sC_1}}{R}=\frac{R_2}{R}+\frac{1}{sRC_1}$$

Please note that the resistor R is the resistance which is effective for feedback (here: \$R=R_1 \parallel R_{\text{lower}}\$). More than that, it is important to know that the circuit works NOT as a stand-alone circuit because there is no DC feedback. However, when used as part of an overall negative feedback loop the controller has a stable bias point - provided \$V_{\text{ref}}\$ is matched to the voltage division produced by $$\frac{R_{\text{lower}}}{R_1+R_{\text{lower}}}$$