Hi Salvador,
Thanks for the details. A couple of details may help narrow this down: are the headphones paired with another device and does auto-connect fail after a normal startup too or only after sleep or hibernation?
For testing, turn off Bluetooth on any nearby phone or computer previously paired with the headphones and temporarily disable Connect to 2 devices simultaneously in the Sony Sound Connect app. This will show whether another device is taking priority during reconnection.
You can also check the Bluetooth adapter in Device Manager > Properties > Power Management and clear "Allow the computer to turn off this device to save power", if that option appears. Then perform a full shutdown by holding Shift while selecting Shut down and test again after powering the PC back on.
If it still happens, please let me know the Bluetooth adapter model and driver version, along with whether the headphones reconnect normally to other devices.