I can confirm that. The following 8 hours I activated only WLAN and used Android support only several minutes:
the accumulators decreased in 8 h from 50% to 19% → that is a factor 6 times faster than with WLAN deactivated.
I hope that the next software-update brings a significant improvement in this issue.
Idea:
Before that phone I used a Moto G 9 play which has a very nice feature:
If you put down the phone face down (display on the table) → “do not disturb”-mode is automatically activated. When you pick it up later, it is at once in the normal state again.
For the Xperia 10 III would a similar behavior be very useful :
If you put down the phone face down, the flight mode should be activated automatically. When picking up it should be deactivated. (If you lay down the phone face up, nothing should be done.)
→ This would save a lot of power without tapping the settings on the phone!