Nothing wrong with thinking out loud. It’s good to question things like this. Let’s take a look at the relevant scriptures:
20 Keep praying that your flight may not occur in wintertime nor on the Sabbath day; 21 for then there will be great tribulation+ such as has not occurred since the world’s beginning until now, no, nor will occur again.
Now, why would someone that observes the Sabbath not want their flight to be on the Sabbath? Would the act of fleeing break the law? Or could it be that in most cases when you go somewhere you usually pack clothing and supplies? I could see that as a violation. But in the context that Jesus is referencing, are we to expect that we are going to literally have to go somewhere, or is it figureatively?
15 “Therefore, when you catch sight of the disgusting thing that causes desolation, as spoken about by Daniel the prophet, standing in a holy place+ (let the reader use discernment), 16 then let those in Ju·deʹa begin fleeing to the mountains.
Based on the above scriptures, I don’t think it is meant to be taken literally. At last I hope not. I don’t live near any mountains! I don’t know if this helps, but it’s what popped into my head. It still doesn’t explain why he said “Sabbath”, unless he was just trying to keep things in a context the people at that time would understand. But why bother saying it at all? He could have just as easily not said it and they would have understood the overall message.