What is stored
Two things, both in this browser’s local storage: your colour-theme preference and any custom palette you build. The mode you pick on the neighbours page is handled by code running in the page itself; it is never sent anywhere, because there is nowhere for it to go — this site has no accounts, no login and no backend.
What is not
No analytics, no advertising, no third-party scripts, no embedded players and no fingerprinting. The site loads its own stylesheet, its own fonts and its own modules, and its content security policy is written to refuse anything else.
Deleting it
Clear site data for this domain in your browser settings and your theme choices are gone. There is no copy anywhere else to request the deletion of.
Server logs
Requests are served through Cloudflare, which keeps standard operational request logs. Those are infrastructure records of which pages were fetched; the modes you pick never appear in them.