For the comfort of the viewing audience, camera movement in immersive media should have some kind of stabilization. This could be the built in gyro found in consumer cameras such as the Insta360 One X2 or GoPro Max, or specialist 360 hardware stabilizing solutions such as the Moza Guru 360Air. Professional cameras such as the Insta360 Pro2 have usable stabilization built into the camera. The key requirement with external stabilizers is that they must not obstruct the fisheye lens' wide field of view and access to ports on the camera body.
Sometimes the most economical way to move the camera is to simply attach it to a moving object that fits the story. This could be a wheelchair, inside a moving car, on the deck of a boat; these are all examples where the motion is caused by or related to the object moving the person (in other words the camera) in the scene. As well as delivering dynamic moving shots, these also provide a point of visual stability which can help prevent motion sickness. This is known as the ‘cockpit’ effect, and it can be surprisingly effective. Not only does finding story-driven ways to move the camera help the audience become more immersed in the narrative, it's often a lot less expensive.