I'm glad you're focusing on the core part of the circuit. There's no point in adding more (current limiting, CC/CV indicators) until you build a working foundation.
Review the
golden rules of op amps; especially the 3rd where the difference between +/- inputs should be zero in a steady-state negative feedback arrangement.
Below, I walk-through how the voltage regulation works via negative feedback (refer to the simulation in your last message and your latest schematic). Lets start...
a. The default position of the darlington Q1 is fully on via R3 (1.2K) to +12V (ref+bias supply).
b. If the darlington is fully on then the unregulated source voltage (to its left) is let through to the output (right side) with minimal voltage drop.
c. Notice the GND symbol on the +OUTPUT that ties the GND of the ref+bias supplies (+12V, -12V, +5VREF) to this point.
d. If the full unregulated source voltage is let through, then the -OUTPUT is the negative of the unregulated source voltage (in our case the battery symbol) relative to the same GND.
e. We have a resistor divider between the lower -12V (fully unreg. source voltage), the voltage adj. pot R37, R15 (15K), and +5VREF.
f. Given that +5VREF being relative to the same GND point on +OUTPUT,
if the fully unregulated source is let through, that makes it 12V (full unreg. source voltage) + 5VREF = 17V across the pot R37 and R15.
g. Lets say the pot is half-way (25K), then we have 17V across 25K+15K=40K.
Q: What's the voltage at the mid-point between them?
A: 25K/40K=0.625*17V=10.6V (lower) and 17V-10.6V=6.4V (upper)
h. The +5VREF is like an anchor; it's always +5V from GND (via TL431 regulator action).
Given the upper part of the divider being 6.4V to the mid-point, that places the mid-point below GND (+5VREF-6.4V=-1.4V).
i. The mid-point is connected to +Vin of the op amp, the -Vin is tied to GND.
So now +Vin is lower than -Vin! This causes the output of the op amp to swing negative.
j. The negative-going op amp output flows through the diode to turn-on Q2 (PNP),
which lowers the current to the darlington (via Q2 winning against R3),
which (Q1) is no longer fully-on (acts like a growing resistor with a growing voltage drop lowering the voltage going from left to right side),
which lowers the voltage between R15+pot divider,
which lowers the voltage on the upper and lower legs of the divider to the point where the mid-point is no longer negative WRT -Vin of the op amp.
k. The op amp will closely watch any difference between +Vin and -Vin and give a negative kick or back-off (output a positive voltage) to let R5 turn-off Q2, letting R3 turn-on the darlington a bit more.
l. Until you change the the adj. pot and the op amp needs to seek a new equilibrium.
m. Nothing is instantaneous. The unregulated source voltage takes time to ramp up, the op amp also takes time to swing positive or negative, etc.
The actions above will kick into regulation as soon as +Vin is lower than -Vin and won't let a -1.4V difference happen.