I'm working in KiCAD and have this through-hole connector. For some reason I'm not able to get the ground planes connected with spokes other than pin 1. I checked the zone layers for the pins, and clearance settings for the pins and can't seem to find what's wrong.
For a test set the clearance on the ground layer to something smaller.
Also you can remove "thermals" and set it to "solid".
(edit the properties of ground fill)
It looks like the connector has a clearance that is reasonable but your fill is set to twice that much.