So, I've noticed that even the current backpack fills up pretty fast when you're mining or harvesting or the like, yet an unlimited backpack would likely not fit the aesthetic (as no farm sim has had one) and would be another "unrealistic to the point of being silly" thing and/or a game breaker. So, introducing your very own (smaller) Merchant's/Traveler's Cart as an idea. It would be a portable wheeled cart that gives you sixty slots for your harvesting, mining, foraging, or other needs! The downside would be that carrying it would be a small reduction in speed (so idea being it would be capable of being switched out with the backpack for situations you wanted to be faster) and that buying it would be one million gold. Once you bought it, you could also not just use it for storage/delivering items (if you want to give everyone a present in a day, etc) but also to sell items at a slightly higher price and without having to find the exact buyer for them, as you currently need to do, albeit taking time that could be used elsewhere while you wait for your customers (think of Earthbound's Burglin Park or Harvest Moon A Wonderful Life's food stand...) and if you sold enough, you could get an achievement. Good idea? I think so, though implementing it might be an issue.
How about being able to use the Minecarts as storage as well? So they effectively become chests (all of which share the same inventory) as well as modes of transport. Or, in the Mines, you can encounter minecarts to deposit items which end up in a main cart up top for later retrieval. Of course, there'd be a max capacity and once reached you wouldn't be able to deposit any more.
Idea being someone sells it to you, perhaps the merchant herself or Pierre - idea being the merchant or Pierre has an event where either is "I've noticed you're coming up in the world, blah blah blah, do you wanna buy the cart I started with?" and after that event, it becomes buyable from whichever one is selling it. Or Robin makes it... And an additional idea - buyers would occasionally pay way more for artifacts than the shipping bin does as a lucky random event, as happens in the real world with antique shops etc. This would make artifacts a cool item beyond simply things to give one time to Gunther and then trash after that - that doll you dug up or that dwarven computer for example? Someone wants that and they're willing to drop a few thousand gold or trade a really good item for it.