Motorcycles

You'll have to go with a tail bag I suspect.

We run two of these: https://www.aliexpress.com/item/1005008933844155.html Not explicitly that link, but that "model" - you'll see a bunch with different logos, some without. I also managed to pick one up for really cheap off Amazon so it was cheaper and got delivered faster than my AliExpress one. It does expand a bit and I was able to squeeze a Shoei Neotec III medium inside (!). Approximate capacity is 11-15L.

I've just ordered this one from AliExpress: https://rhinowalk.com/products/23l-35l-abs-hard-shell-tail-bag-with-expandable Will have to see how it fits on the bikes at home, but 23L will absolutely be able to fit groceries.

Lol the saddle bag melting should be the least of your worries. You're coating the bag and everything inside of it with cancer causing chemicals. Even if it didnt melt you'd be eating straight cancer for dinner

After finally being able to watch the video, I'd never expect a material bag to tolerate that - it's directly in-line with the exhaust and even slightly above it.

Even if the bottom of the bag were an aluminum plate, I think that plate would simply transfer heat into the bag.

It would require something like a lower plate, an air gap, and another plate, to ensure a heat break.

Or a plate on the exhaust directing the output more horizontally for the length of the bag.

Also, sorry this happened, that's a bunch of crap from the manufacturer.

Well that sucks. I'm trying to remember where my saddlebags drape, but they're definitely not in any possible line with the exhaust vent, nor are touching. I think my actual panniers made for the bike have a metal shield that sits between the exhaust and the pannier sort of hovers over and to the side of the exhaust.

Maybe your exhaust is just super special in how much heat it throws out.

I don't think any bag can tolerate the heat of exhaust.

When moving on the road, it gets pretty hot - even rigid bags would sag

That looks like it was sitting on the exhaust?