Big voltage drop on output of voltage regulator on adding load
I don't see any properly-measured current waveforms or inductor voltages .... which would help in the diagnosis.

But I do see your inductor is broadside to a bunch of discrete parts in the loop that will get crosstalk and maybe a false per-cycle current-limit being detected.



Demo board is facing a bunch of thermal ground vias which diverts the radiated EMI noise to minimize crosstalk and instability.



A BIG NOTE: Always choose an orthogonal orientation for the switched inductor to other nearby traces and parts and don't put them broadside near the RF high current inductor.