Can I change the width of the Solution Configuration combobox in the IDE?

Yes you can. you must enter in "add or remove buttons -> customize". Inside the commands tab select the button you want to customize and click "modify selection" you change the width value there. Take a look here

http://visualstudioextensions.vlasovstudio.com/2014/08/14/adjusting-the-width-of-solution-configurations-drop-down-list-in-the-visual-studio-toolbar/

Same same but different in VS 2019:

1. Go to 'Tools --> Customize'.
2. In the 'Commands' tab, select 'Toolbar: Standard'.
3. Select 'Solution Configurations' and click 'Modify Selection'. You can adjust the width there.