It depends on the Xbox and on which games. Xbox consoles expand through external USB storage rather than internal drives, and on Series X and S, only backward-compatible titles play from a USB drive, Series-optimized games need internal storage or the expansion card.
Microsoft's support documentation states that you can connect an external USB 3.1 hard drive or SSD to an Xbox Series X or S and play Xbox One games from it, including backward-compatible Xbox 360 and original Xbox titles. Those run directly from the external drive with no copying step.
Titles optimized for Xbox Series X and S do not. Those run from the console's internal SSD or from a Storage Expansion Card, which is a proprietary module rather than a USB drive. A USB drive can still store them, so you avoid re-downloading, but you move them across to play.
On an Xbox One, the rules are simpler: an external USB 3.0 drive plays games directly, full stop. For that generation an external hard drive is a complete solution.
A bare 3.5-inch BarraCuda does not connect to an Xbox. The console expects a USB drive, so you would need an enclosure and a power supply, which turns a simple purchase into an assembly project with no cost advantage over a purpose-built external drive.
If you want to use a BarraCuda this way, the sensible route is a 2.5-inch model in a bus-powered enclosure, or simply buying an external drive that already is one. Our external drive coverage prices those live.
The recording technology is close to irrelevant here for the same reason it is on a PlayStation: installing is a long sequential write, playing is reading, and there is no array and no rebuild. Shingling does not hurt this workload.
Because current-generation titles are not played from the USB drive, what you are buying is a large, cheap parking space that saves re-downloading tens or hundreds of gigabytes. That means cost per terabyte is the thing to optimise, and the interface specification barely matters.
A Storage Expansion Card is the alternative for playing Series-optimized titles from expanded storage, and it costs several times per terabyte what an external hard drive costs. For a library that is mostly backward-compatible, the external drive is clearly the better purchase.
Buy more capacity than you think you need. Modern installs are enormous and the entire point of the drive is to avoid re-downloading them.
No. Xbox consoles are not designed for internal drive replacement by users, and expansion is through external USB storage or, on Series X and S, the proprietary Storage Expansion Card. A bare internal drive is the wrong product for this.
Only the backward-compatible ones. Microsoft states that Xbox One, Xbox 360 and original Xbox titles play directly from a USB 3.1 drive, while titles optimized for Xbox Series X and S run from the internal SSD or a Storage Expansion Card. A USB drive can store them, saving a re-download.
Not meaningfully. Installing is a long sequential write and playing is reading, with no array, no parity and no rebuild. The workload that exposes shingled recording is simply absent on a console.
For a mostly backward-compatible library, the external hard drive, by a wide margin on cost per terabyte. The Expansion Card is worth it if you play many current-generation titles and do not want to move them across before playing.