Disney had a refillable bottle for sale with the merchandise with the badges - never misses a trick.

Mine is nicer and I know it's water tight.
You can bring bags into panels.*

In the past they also provided a "free" tote when you enter to stash all the giveaways/purchases, but they have also been getting smaller and cheaper in quality. I generally take a roomy tote to carry my stuff and then pack a smaller eco bag to carry purchases/giveaways. They have offered a Bag check in the past, but generally it's for large purchases, if that makes senses.
*There is a size limit in the Things to Know section on the website: Suitcases, bags, coolers, or backpacks, with or without wheels, larger than 24 inches long x 15 inches wide x 18 inches high (61 cm x 38 cm x 46 cm) are not allowed.
https://d23expo.com/things-to-know/