Since it pushes but doesn’t pull you’ll need to replace one or more of the linkage pieces in the column.
From the ignition lock cylinder down to the ignition switch is a two piece linkage allowing the column to tilt yet still push & pull.
The two pieces are plastic, one of them is broken.
To gain acces to them is a pretty major disassembly of the column. Get a repair manual or have someone do it who’s familiar already.