You should order a garbage bin that goes with the pull-out that you bought, so it will fit. Our Innermost cabinets came with Hafele trash bins:

Hafele Bottom Mount Trash Can

They use standard 13 gallon kitchen trash bags, as do most kitchen pull-out trash cans.

I used to have a SimpleHuman standalone trash can which took more form-fitting SimpleHuman trash bags. Those fit better than standard bags, but I don't think these cans have anything equivalent.

I can only speak about Innermost as well, but ours came with Knape & Vogt. We've got an 18" with drawer above and it's got 2-35 qt cans.

Other varieties of Innermost cabinets have a single 35 qt or a single 50 qt or one of each.

52 qt would be 13 gallons, so a tall kitchen bag is safe for any of these. I don't know if this will be my final solution, but I rolled off about 8 bags and tucked them down in between the two cans and stored the ginormous box in a high cabinet.

Thank you calumin and cal quail. My mind is wandering to these details now. :)