Hi Jack_YH.
You're approaching the point where backing the Mac up via Time Machine and then erasing and restoring from that backup without restoring the errant user directory may be the only supported path. But before you undertake that process, try this.
Take the Jack folder that is still in the Trash and drag it to the desktop. In a perfect world, the item called Library will exist as a folder inside of that and then the item called Application Support will exist as a folder inside of the Library folder. If the items in the trash do not currently nest this way, then assemble them that way on the desktop. Then, drag the Jack folder with the other two folders inside of it to Macintosh HD > Users.
Once that is done, reboot the Mac and then check at System Preferences > Users and Groups and see if it appears as user account which you can delete via that pane.
If that is also not effective, then you'll want to:
1) Back the Mac up using Time Machine if you have not already done so.
Back up your Mac with Time Machine - Apple Support
2) Boot the Mac using macOS Recovery.
About macOS Recovery - Apple Support
3) Once booted to Recovery, use the Disk Utility app to erase the volume called Macintosh HD.
Erase and reformat a storage device in Disk Utility on Mac - Apple Support
4) Reinstall macOS.
How to reinstall macOS from macOS Recovery - Apple Support
When you reboot after all of that, the system should treat things as if this were a new Mac just being set up. When the Setup Assistant asks about restoring data, choose the Time Machine backup. You should get a window which allows you to customize what data gets restored. Next to the line for Users, you should see small triangle. Click that and you'll see all of the user accounts that the system believes to exist with checkboxes for each one. Just don't click Jack user account and it should be ignored when data is being restored.
The first set of steps has only a small chance of doing the trick here. But it is way less time intensive and far less intrusive and is the best path to take if you're just trying to get to a place where those files can be deleted from your Mac.
Cheers.