I think over the years Sears had quite a few diverse suppliers.
The Sears Steyr 3 speed bikes are nice. They can make a good and useful city bike. If you want to go crazy, hotrodding them a bit with alloy rims is worthwhile.
A long time ago, I had a French made "JC Higgins" of unusually high quality, bordering on constructeur. It was probably 1950s, and it had a mixte/ladies frame, crazy French chain guard and fenders etc. I've never seen another one. Has anyone? This was a thrift store find maybe 30 years ago. I didn't keep it long, but wish I had.