One Bag

I don't own these bags, but this is where I would start. Decathlon offers decent quality at decent prices, and it's a good chance to try something out and see if it works for you.

Duffel, 40L, 15"x21", waterproof and can be worn as a backpack: https://www.decathlon.ca/en/p/8383299/hiking-bag-40-l-to-60-l-duffel-500-extend Suitcase, 30L, 13"x20", wheeled and can be carried as a duffel: https://www.decathlon.ca/en/p/8753739/30-l-suitcase-essential-black-grey The traditional 40L backpack might be a bit tight for your purpose at 12.7"x21". https://www.decathlon.ca/en/p/8735937/hiking-backpack-40-l-travel-500-organizer-black

I personally have an Osprey Farpoint that I really like. It's 14"x22" and can be carried as a briefcase or a shoulder bag or a backpack. It's quite a bit pricier.

I think you'll want to make sure that whatever you get is relatively square (given your purpose) and that it opens flat. Let us know what other considerations you have, and what you finally decide to try. Nothing beats taking a few scores to a local store and trying a bag in person.