Model Viewer Camera Rotation

I've been working in Unity for quite a while, and I hate asking simple questions like this, but quaternions still baffle me.

I need to make a CameraController with rotation functionality. The camera will have focus on different objects at various points, and I need the ability to rotate around the object (left, right, up and down).

Right now, this is what I have:

  public void RotateRight() {
         transform.RotateAround(focusObject.transform.position, Vector3.down, rotationSpeed * Time.deltaTime);
     }
 
     public void RotateLeft() {
         transform.RotateAround(focusObject.transform.position, Vector3.up, rotationSpeed * Time.deltaTime);
     }
 
     public void RotateUp() {
         transform.RotateAround(focusObject.transform.position, Vector3.right, rotationSpeed * Time.deltaTime);
     }
 
     public void RotateDown() {
         transform.RotateAround(focusObject.transform.position, Vector3.left, rotationSpeed * Time.deltaTime);
     }

Ultimately, these functions will be called by UI interactions (thus their segregation).

The Up/Down and Left/Right work just fine, so long as their not used together. As soon as I start combining rotations (or rotating Up/Down after Left/Right, etc), everything falls apart so to speak.

I'm not sure how to explain how I want this to function, so better to just show an example: https://sketchfab.com/models/08d80ef4bc2d4ab3a57b5b3ff227856d

This is easy to do if I rotate the OBJECT, and not the camera, but that is not an option for me.

In a nutshell, how would I go about duplicating the rotation functionality of the sketchfab viewer?