Poppets are treated as their own characters, and can be viewed alongside your normal characters! On their character page, find the Update Design button under the Settings on the sidebar. Hit Create Request on the resulting page to bring up the design editor. This is where you can upload their new masterlist image and add their traits!
Don't forget to attach your items in the Add-Ons tab if you're including any customizations!
Once you're satisfied with everything, you can Submit Request and it'll be sent to the moderator team for review. Upon approval, the new character will appear in your character list and on the official masterlist!
If you're unfamiliar with poppets, see their guide.