You could require a login after someone has added at least 5 objects and/or spent at least 5 minutes making edits. This makes sure that if data is lost, it's nothing that can't be easily recreated.
After at least 30 seconds of activity, you can display a prominent banner at the top of the page that says "make a free account to ensure your work is saved". Then it's clear that your ability to retrieve their data upon their next visit is a favor and not something they're obligated to. It's not exactly the same, but you can look at CoderPad's sandbox notice as inspiration for how to word this: https://app.coderpad.io/launch-sandbox (Note: you'll only be able to make one sandbox per cookie, so visit this in incognito mode)
To address scaling, you can probably limit the total number of "logged-out users" who are currently editing. If more users visit the site during the same time period, require them to make an account, just like you are now. If you're worried about users expecting a playground and getting confused, you can look at Google Docs's "This is getting a lot of traffic, you're in read only mode" notice that appears when more than 50 people are visiting a doc as an example of how explain the situation in an easily understandable way.
Now that you've properly set user expectations, you can clean house whenever and it should be okay.
btw, I just tried out this tool and I think it's awesome for a lot of the reasons mentioned in the top replies. Hope some of this is helpful + wishing you best of luck!