Analyzing the schematic for the 4047, you can see that if ASTABLE is high then the quad NOR will be low no matter what is happening on pins 4,6, 8 so those are actual don’t care pins, as they don’t affect anything but other inputs to the NOR. This is why changing pin 6 had no effect.

Your OSC is oscillating as expected so the internal CL and CL_BAR clocks should be working.
Your Q is stuck low and Q’ high. With Q low that should cause the 2-input NAND gate feeding the final flip flop’s D input to go high and Q should flip on the next clock, yet it remains stuck low.
The only thing (other than a bad chip) that would cause this symptom is if the EXT RESET pin 9 was high: that would keep the final flip flop into the state you describe – Q low, Q’ high.
So the only explanations I see are:
-you’ve wired pin 9 high by mistake, or
-you’ve wired pin 9 low but there’s a bad connection to the actual pin and it is in fact high, or
-the chip is bad
**** EDIT, a few hour later ****
Upon further reflection I realized the "pin 9 stuck high" theory did not jibe with the brief blink of the Q LED on power up: if pin 9 were high then that LED would never light.
That left "bad chip" as the only answer but this is a very unsatisfying answer.
So I went through my ancient stash of ICs and found a CD4047B and quickly wired up your circuit on an equally ancient superstrip breadboard.
And it didn't work - not exactly your symptom but something clearly not right. I checked the wiring, it looked fine. Then I beeped out with a multimeter the legs of the resistor, cap, diodes, etc to the actual 4047 pins just to make sure and lo, one pin wasn't making a connection. I removed the 4047, polished up the pins with DeoxIT, put it back, connection was now good, and voila, the circuit works fine. OSC blinks and Q and Q_BAR blink at half rate.
So your circuit is fine, you likely just have a bad connection or a wiring mistake, simple as that. I think this is more likely than a "bad chip".
Don't trust you breadboard connections - do a continuity check from each of the 14 pins to where you think they should be going.