@cheng-jin-11
Unfortunetaly I don't own a Xbox at all, so my experiences with it are very limited.
But you say it shows up as an USB storage? Because when I looked up a german manual how to prepare a HDD for a Xbox 360 it first shows as an "USB Storage Device" but finally it is entitle with "Memory Unit", when the process is finished. So it could mean by formatting it via PC you are only half way through.
As far as I understood the process there are two options to do it - via PC or via Xbox itself. The manual I found used both method to ensure everything is setup correctly in the end. I will try to translate the process as good as possible:
Step 1: Connect the USB HDD with your PC
Step 2: Format it with fileystem "extFAT" - the plan is to make it absolutely unreadable for the Xbox, because the correct filesystem would be "FAT32", but for now, use "extFAT"
Step 3: Connect the USB HDD with your XBox 360
Step 4: Go to My Xbox --> System Configuration --> Storage (for now, the drive should show up as "USB Storage Device")
Step 5: Select the "USB Storage Device" and choose "Configure Now" to let the Xbox format the drive with FAT32 automatically
Step 6: A warning may appear about performance issues. Just ignore it.
Step 7: If formatting is finished the device should now be named "Memory Unit"
To test it, they suggest downloading some common media file the Xbox can play to the HDD now via the PC. The media files should then be playable via My Apps --> Video/Music/Picture-Library
This is the German manual, but it has English screenshots in it, maybe it helps anyway if you are stuck:
https://de.wikihow.com/Eine-Festplatte-zur-Benutzung-mit-Xbox-360-formatieren
Hope this will work. Because the Official XBOX Seagate 2T Hard Drive you have should really be recognized as a high perfomance device for the Xbox 360. Is it this external one with the Xbox branding and the green cover and black casing? https://arstechnica.com/gaming/2015/08/seagate-unveils-expensive-green-2tb-hard-drive-exclusively-for-xbox-one/
The article says it is an exclusive Xbox One HDD, but on the website Seagate is advertising it for the use for the Xbox 360 also. So if everything fails, you could ask their customer support why the heck your drive isn't recognized correctly by your Xbox 360 - they should now which conditions must be met to do so.
Best luck 🙂