Untethered jailbreaking is the only option that matches all key characteristics described: the device can reboot normally without needing a computer, and the jailbreak remains active after the restart with kernel-level modifications still in effect. In CEH-aligned mobile security concepts, the main difference among jailbreak types is what happens after a reboot.
A tethered jailbreak requires a computer to boot the device at all. If the phone restarts without being connected to a computer, it will not complete the boot process. That contradicts the scenario, which explicitly says the device can fully restart without requiring a computer. A semi-tethered jailbreak allows the phone to reboot without a computer, but it boots into a non-jailbroken state, meaning elevated privileges and kernel patching are not active until re-enabled through a tool. A semi-untethered jailbreak is similar in that it can boot normally without a computer, but the jailbreak does not persist automatically; it typically requires re- activating the jailbreak after each reboot to regain kernel patching and privileged access.
The scenario states the restart occurs while still "maintaining a patched kernel" and continuing access to protected filesystem data, which indicates persistence across reboot. That persistence is the defining feature of an untethered jailbreak. From a defensive and assessment perspective, this is considered higher risk because it provides continuous post-reboot privileged access, increasing the window for data access, tampering, and persistence mechanisms compared with reboot-reset jailbreak states.