Would I use something like this?

You may be able to remove the drive, and use an alternative SATA-to-USB adapter (the portable HDD is effectively a 2.5in Laptop HDD + a SATA-to-USB adapter). Though, sometimes the drive is formatted in a properitary format that can only be read properly by the manufacturer SATA-to-USB.

SATA-to-USB: https://www.amazon.com/Sabrent-2-5-Inch-Adapter-Optimized-EC-SSHD/dp/B011M8YACM

If you end up needing to use the original hardware, you could purchase a 2nd drive of the same model, and use the adapter from that one to recover data from the original drive.

To figure out how to take apart the portable drive, give a YouTube search for "seagate portable shuck", "shucking" is the term used for removing a hard drive from a portable-drive, and using it as non-portable, and will give you a good search point for finding videos of taking apart the device.

This should do it: https://smile.amazon.com/dp/B011M8YACM

But first, there's an extra piece you have to pull off that HDD. I think you have some kind of Data adapter still attached. Once it's off, you'll see the standard sata L-connectors.

You should probably open it up and dig the ssd out of it, then put it in a SSD Adapter

Get your self one of those USB to laptop drive adapters.

https://www.amazon.com/Sabrent-2-5-Inch-Adapter-Optimized-EC-SSHD/dp/B011M8YACM

You can use a USB to SSD adapter.

https://www.amazon.com/Sabrent-2-5-Inch-Adapter-Optimized-EC-SSHD/dp/B011M8YACM

All you need is one of these and then plug the thing in your Xbox like a usb stick