If I open /org/gnome/shell/extensions/caffeine/ in dconf-editor, it
shows the settings as "Keys not defined by a schema".
https://github.com/eonpatapon/gnome-shell-extension-caffeine/blob/22a89835f12ff11534492e5d577c1e2401fa080c/caffeine%40patapon.info/schemas/org.gnome.shell.extensions.caffeine.gschema.xml#L19
includes a path attribute, so I think the schema is correct.

Would adding a line like
https://salsa.debian.org/gnome-team/shell-extensions/gnome-shell-extension-dash-to-panel/-/blob/f4472ed6437f7d33a31633f71ba28287ad73196f/debian/install#L1
to caffeine's Debian package make the schema available to dconf-editor?