So, I rechecked. After purging everything and building again, I checked the chroot. And what did I find?
A lot of entries with "trixie" in */chroot/var/lib/dpkg/info which are mostly "*.postinst" files. Where are they coming from? These are all from installed packages, but all packages should be from bookworm and not trixie. Of course I also checked sources.list in chroot, and all are "bookworm", so IMO there is no reason, why anything should contain "trixie". Bookworm does not know of trixie. Strange..... I believe, THIS is the reason, why it wants to install grub-efi-amd64- unsigned: false entries in */chroot/var/lib/dpkg/info. Question: Does the live-build script get any information from the native installed debian? Then this would explain, why it got false informations: I played with the installed native debian, just to look, which packages are new in trixie. Thus I changed my sources.list (in the native debian) temporarly to trixie (and then back). Of course my native bookworm still got the "*.postinst" files below /var/lib/dpkg/info. And if "lb build" will copy THIS to the chroot, then it will explain, what happens. However, this is just a guess. Maybe one of the live-build-maintainers knows more. Does this help? Best Hans