Hi, thank you for the detailed report. Your configuration is correct.
matterbridge-daikin-onecta exposes power and operating mode through the Matter Thermostat SystemMode attribute. Gladys 4.82.0 does not support this attribute yet: it currently handles the room temperature and heating/cooling setpoints only.
This explains why the temperatures are available, while On/Off and Heat/Cool selection are missing. Fan and Boost are separate Matter endpoints, which is why Gladys can display them.
Unfortunately, there is currently no Matterbridge configuration that can work around this. Support for Thermostat.SystemMode needs to be added to Gladys. Your report is useful for implementing and testing it.
Related discussion: Matter - Climatiseur : Gestion des modes