You say that you use the USB adapter to connect the external drive to your MacBook Pro, only to find the external SSD not mounting on your Mac, right? Are you ensure that you connect the external disk to the USB adapter and meanwhile the USB adapter is connected to your MacBook Pro tightly and correctly?
A loose connection is always the case that makes the external hard drive not mount on Mac.
The 2021 MacBook Pro is designed with Thunderbolt 4 ports. Maybe the USB adapter has some problems or is not compatible with your Mac ports, you can change it to another one.
If the external hard drive not mounting issue is not caused by the connections. There's a possibility that the system glitches or third-party apps, especially some USB defenders, block the external disk being mounted.
You can update your Mac:
- Click the Apple menu > System Preferences > Software Update.
- Check if there is an available update.
Besides, check if you've installed the USB Defender or similar apps that protect the security of your Mac. Reset the settings to allow Mac to mount the external devices on your Mac.