When dealing with the issue of constrained bone positions changing after modifying a binding constraint, there are several strategies you can employ:

1. Copy and Paste Constraint Settings: Since Spine 4.2, you can copy and paste constraint settings. This can help you reconfigure constraints more easily after moving bones. Select the constraint name in the tree view, press Ctrl+C to copy, then select the target constraint and press Ctrl+V to paste.

2. Adjust Constraint Order: The order in which constraints are applied can affect the final position of bones. If a constraint is applied after another that moves the target, it can cause unexpected behavior. You can change the order of constraints by dragging them in the constraints list. More information can be found here.

3. Keying Constrained Bones: If you need to key the constrained bones, ensure that the transform constraint is set correctly. If the transform property is 100% affected by a constraint, Spine will calculate the constrained local transform and key that. This feature is available from version 3.6.00-beta.

4. Resetting Constraints: Sometimes constraints appear to stop working because they are overridden by other constraints. Resetting the constraints order or changing it manually can help solve this problem.

5. Manual Adjustment: In some cases, manually adjusting the attachments in the viewport to the correct position can be simpler than changing the parent of attachments in the tree.

6. Transform Constraint Settings: Ensure that the transform constraint is set to local and possibly relative if you are experiencing issues with IK scaling or other transformations.

By following these steps, you should be able to manage the position changes of constrained bones effectively.

When you change weights and the bones move, it is because you've transformed the bones since binding them to a mesh. You can use the Update button to update the bindings to the current bone transforms.

That is shown in this video, at ~ 13:45:

There are many other videos that show it in more detail, on this page click the Update bindings filter:
https://esotericsoftware.com/spine-twitch