What is stored in your browser
Two things, and both stay on your own machine. Your chosen theme, light or dark, and the codes of any voices you built yourself. Both live in local storage, not in a cookie, and neither is sent anywhere.
One short-lived cookie exists during a request to carry the puzzle your browser solves to prove it is not a script. It expires within minutes and holds no identity.
Why there is no banner
Consent rules apply to storage that is not strictly necessary for the service you asked for. A theme choice and a list of your own voices are settings you made; the request cookie is required for the request to work. None of it tracks you across sites, and there is no third party to share it with.
A banner would ask permission for something that is not happening.