Why does the inverting amplifier not work with my separate circuit as an input?
As asked in the comments, are you only connecting the circuits with a single wire?

That won't fly.

You're also markedly changing the first circuit - if you get a signal you are happy with at the "blue point" with the LED, try leaving the LED in place and connecting the "blue point" to R4 and the left hand circuit battery negative to the "0 V" of the right hand circuit.

If that works you can try with the LED removed (if the above is "changing two things" from how you have been trying it.)