When I do this, the mesh extrudes evenly to either side of the faces instead of to inside or outside. Is there a setting or to
ggle to change this?
The thing is, you have too much selected!
This is how it should be. Look at the white dots (selected, in your case: orange) and the black dots (unselected):
Now this happens when scaling (as it should):
But you must have Extruded, canceled (which doesn't cancel the extrusion, only the 'Move" that would normally follow the Extrude) and then selected 'everything' and extruded again:
Look at all the white dots (selected Faces). When Scaling now, this happens:
That shouldn't be the issue, you have double vertices in your screenshot ( more than one vertex at the same position), which can be seen by the black dots at the edges; they are the centers of Faces, You should use A, M > Merge by Distance! (I recommend you do this even if things appear to be working correctly now.)
In fact: double vertices (solution : M > Merge by Distance) and flipped Normals (solution SHIFT+N) are together responsible for (a lot) more than 90% of all modelling issues.