This might be useful for someone running Debian testing and wondering about high CPU usage and related high power consumption.
I am running Debian testing with the GNOME desktop on a FW 13 AMD, although Intel machines might be similarly impacted. I have been following the various threads on power management with great interest and using powertop to monitor power usage more than I usually would and discovered over the course of the last couple of weeks that power consumption has jumped considerably, often to well over 15 KW, leading to shorter than expected battery time. Both powertop and top reveal high CPU usage from /usr/libexec/packagekitd. It turns out several upgradeable Debian packages cannot be upgraded at the moment (mid-April 2024) due to missing dependencies. The testing version of gnome-software relentlessly calls packagekit to try again, causing a spike in CPU usage (see "Loading Updates" keeps repeating endlessly on Debian (#2462) · Issues · GNOME / gnome-software · GitLab). Using apt or aptitude to hold the upgradeable packages in their current version keeps gnome-software from trying to install them and brings CPU usage back down. Apparently this behaviour is fixed in the version of gnome-software that will eventually be released to testing.
I hope this info helps someone concerned with short battery times on their Framework running Debian!