There’s the on_boot function. See here:
But you still have to wait for the first reading from the sensor.
Both my mailbox and lane gate binary sensors wake for 2 minutes but as they only have to wake when something changes (or every 6 hours to report the are still there) they spend 99% of their time asleep and one 18650 cell and a 5W 5V solar panel runs them forever.
It’s a different story for analogue sensors that have to report in regularly as you are discovering.
Your previous 10s wake 20s sleep duty cycle is the exactly equivalent battery drain to 2 min wake 4min sleep. So if you designed your battery for that, then longer wake and sleep should be the same average drain. It just means you only get an update every 4 minutes. And to be honest even that is probably overkill for a compost heap. You could take a reading every 15 to 30 minutes and get the same sort of graph, except at the the times right when you turn the pile (if you ever do).