The timestamp-change (and timestamp-update) profile is another solution for the 1st “Task: Access the item lastUpdated timestamp”, thanks for pointing this out.
In order to achieve the next two tasks (“Ingest the real lastUpdate/lastChange timestamp” and “Ingest multiple historical states”) I have currently bypassed the native MQTT binding and instead ingest with Habapp and a set_persistence_data (with ModifiablePersistenceService), therefore it does not fit my setup (since I don’t use the native MQTT channels). It should work well though for someone who just wants to know if the sensor sent a recent update and wants to avoid relying on persistence extensions.