Hello,
You should no add any code to enter stop mode 2. I am not sure where you added SCH_Run(0) but wherever this was added, please remove it.
I would suggest to start from the p2p_sever example as it has been delivered without any code change and modify the setting in app_conf.h to have
Set CFG_DEBUGGER_SUPPORTED to 0
Set CFG_DEBUG_BLE_TRACE to 0
Set CFG_DEBUG_APP_TRACE to 0
To make sure the device enter low power mode, you may output the system clock on the MCO ouput and check the signal with either an oscilloscope or a digital analyzer. When the device enters Stop Mode, you should see the clock not toggling anymore in between advertising packets.
You may use HAL_RCC_MCOConfig(uint32_t RCC_MCOx, uint32_t RCC_MCOSource, uint32_t RCC_MCODiv) to ouput the system clock on MCO.
Regards.