I’ll be honest, I’m not sure what to make of Jesus mentioning the flight on the Sabbath. You would think though, that if he wanted us to keep it he would have emphasised it in the Sermon on the Mount. I agree with what you said regarding love covering the commandments, other than the Sabbath. Jesus even added to what the original commandments said when he basically said that lusting after someone with your eyes is the same as adultery. You would think that with him covering all those things, and clarifying what adultery now entailed, he would have said “and don’t forget to keep the Sabbath!”, but he didn’t.
As far as what Paul was teaching, I think that came up in the comments recently. If I remember correctly the answer was that the disciples were probably very careful not to let anyone else see them not observing it. If that was the case, then Paul likely just told them to be careful, but I can’t back that up with scripture.