The main reason you are not seeing ground-fill stitching is that “Connected Layers” only tells an existing via/pad/fill which copper layers it may connect to; it does not automatically create GND stitching vias or guarantee that every layer has a GND copper fill. Your layout is a 6-layer signal stackup, and the design currently shows only a small number of fill/zone objects while DRC still reports many airwires, including GND and PGND, so the ground copper is not fully acting as a stitched, resolved plane system.
Open items:
GND and PGND appear as separate/unresolved ground-related nets in the airwire report.
The board has only a few fill/zone objects, so the intended Top / Mid-Layer 1 / Mid-Layer 4 / Bottom ground planes may not all exist or may not all be assigned to the correct ground net.
Existing vias may be connected across layers, but that does not mean they are placed as a stitching pattern or tied into filled GND copper.
Suggested next steps:
Verify each intended plane/fill is assigned to GND and exists on Top, Mid-Layer 1, Mid-Layer 4, and Bottom.
Decide whether PGND should be tied to GND or kept separate with a controlled single-point connection.
Add/enable actual GND stitching vias after the fills are confirmed.
Re-run airwire/floating-copper checks to confirm GND is fully connected.