After updating to 1.24.0-1577, the device stopped sleeping. In BetterBatteryStats in Partial Wakelocks AquaMail in the first place with an indicator of 100%)) 6 mailboxes are configured: 2 imap push, 4 according to the schedule. In the beta that preceded this release was the same.
After downgrading to 1.23.0-1560, everything turns back to normal.
The ancient device is Samsung Note 3, ancient Android 5.1.1, maybe this is the case. )))