I thought this would have been stored in
scene.tool_settings but it doesn't seem to be. I can access the default keymap value like this:
But this doesn't update after decreasing or increasing the radius any time durring or after you use the tool. Should also mention I'm not interested in accessing the Toolbar version of Circle Select radius property. I'm interested in accessing the radius property of the operator itself (view3d.select_circle). You can demonstrate to yourself how these properties differ by pressing the C hotkey vs accessing Circle Select via the Toolbar and changing the radius value on both.
Presumably the value is being stored somewhere because both the Toolbar version and direct operator radius values are stored separately. Also
bpy.types.VIEW3D_OT_select_circle doesn't seem accessible, so I'm assuming I'm out of luck but thought I would double check.