Editor Gizmo logic question? How do the gizmos move relative to camera

If you use the Sign() of the Dot Product of the camera's right relative to the local axis' right as a multiplier, the problem should be solved fairly smoothly.

(Also, you neither need nor want to multiply by Time.deltaTime in this situation. GetAxis() with mouse input already provides only a per-frame based changed, where a constant value (i.e. held key) would need that scaling)

While there are many ways to make this system more robust (and also require further additional programming to scale input strength with distance to the object), this should help get you on the right track with what you're currently working on:

 float inputScale = Mathf.Sign(Vector3.Dot(focusedGameObject.transform.right, Camera.main.transform.right));
 tempPos += focusedGameObject.transform.right * Input.GetAxis("Mouse X") * moveSensitivity * inputScale;

If you want the strength of the input to vary based on angle...
If you want a low speed at a steep angle, remove Mathf.Sign() from around it.
If you want a high speed at a steep angle, replace Mathf.Sign() with Mathf.Tan() and scale accordingly:

 float inputScale = Mathf.Tan(Vector3.Dot(focusedGameObject.transform.right, Camera.main.transform.right) * Mathf.PI);

^{Note that no further accommodations need to be made in this situation because both inputs for the Dot Product are normalized vectors.}