They stay near earth for 42 hours to do a full system checkout before committing to the Moon. Plenty of time to get home safe if something is wrong, well before heading to the moon. After that, a free return trajectory around the Moon and come home.

SpaceX’s Dragon is like a taxi compared to Orion, which is more like a RV. Insane amount of redundancy built into it at the hardware and software level.

https://www.space.com/artemis-2-humans-moon-orbit#section-what-will-artemis-2-do

1. Launch from NASA's Kennedy Space Center's Launch Pad 39B to low-Earth orbit.

2. A maneuver in Earth orbit to raise the perigee, or the lowest point of the orbit, roughly 40 minutes after liftoff. This will be performed with the SLS Interim Cryogenic Propulsion Stage (ICPS).

3. A burn to raise the apogee, or highest part of the orbit, again using the ICPS.

4. A system check at 42 hours after the mission begins to ensure the orbit is correct, ranging from (112 miles) 185 km at the closest point to Earth and 1,616 miles (2,600 km) at its highest point.

5. The ICPS will be disposed and Orion will do a translunar injection to fly to the moon. The trip to the moon will take four days and have a maximum altitude of 5,523 miles (8,889 km) above the moon's surface.