“A simple, free and powerful way to manage your team's recurring checklists and procedures“ https://www.process.st/ Paid features include 3rd party integrations. (Disclaimer: neither a customer nor employee of the company.)
Do any of these let you re-use your checklists, though? Planner at least is pretty useless for this, as I don't think there is a 'reset all items to un-checked' feature, or even basic stuff like re-arranging your list.
Everything in my comment was describing Planner. You cannot re-arrange checklists on a task in Planner on mobile. And I'm not clear if you were describing Planner in your comment, but I just tested the workflow described and it results in a second copy of my task with the same checklist items checked.