This is a sub-issue of #1910624: [META] Introduce and complete configuration schemas in all of core.
Problem/motivation
#1866610: Introduce Kwalify-inspired schema format for configuration introduced the idea of config schema. The changelog leads to (hopefully extensive) documentation on the format at http://drupal.org/node/1905070. While there are little cleanups planned for the format overall, the current format is a result of months of back and forths, so it should be perfectly fine to apply it more widely to core.
Proposed solution
Create a configuration schema for breakpoint module. Note that this may be one of the trickier conversions.
Schema in place
Schema not yet in place
breakpoint.settings.yml
Breakpoint config entity type
BreakpointGroup config entity type