Your criteria for a bag sound very similar to mine, and I've decided that top handle satchel/bowler bag styles (with a crossbody strap) are my favorite kind of bag. This one can't be purchased on their website anymore, but I have this Furla Alba satchel in black, and I absolutely LOVE it. It's great quality, and I can stuff random things in it as needed. I live in a climate that has very cold winters and snow, and also have 4 young kids, so it's been a workhorse. You can find it relatively easy on secondhand sites. At the very least, maybe try searching for more bags in this style?
https://www.furla.com/us/en/eshop/furla-alba-BTE3FABHSF0001007O6000.html
https://www.furla.com/us/en/eshop/furla-alba-BTE3FABHSF0001007O6000.html