How to scan/fix bad sectors on USB connected Ext HD even if SMART is unsupported w/o buying tools
In general you can't get SMART status of a drive in an external case. Some cases will support it, some do only with vendor-supplied software.

But SMART isn't all that useful. It's good at telling you the drive HAS a problem, not so good at telling you the drive might have a problem soon. And bad sectors on modern (21st century) drives are already mapped out by the drives controller - any sector that doesn't read reliably will just be mapped to a spare sector and you won't know about it.

Was the Seagate running when it was dropped? If no, no problem. They're designed to take some minor abuse when turned off. If yes, and you do manage to detect even a single bad sector then just replace the drive. Any bad sector that reaches user levels means the drive is out of spares, and that's probably because the head crash caused by the fall is now dragging a tiny bit of metal all over the platter.

In short, if you have any doubts about the reliability of spinning drives these days the most cost-effective route is to replace it. At $25-$60 per terabyte it just isn't worth the considerable time to verify the drive.