[UI v2] Edit variables

[desertaxle]

This PR adds the ability to edit existing variables. It repurposes the existing variable dialog to handle edits. Here's what it looks like:

https://github.com/user-attachments/assets/e18aec2a-4393-4ad1-96df-81ae48ee2505

This PR also starts to experiment with colocating hooks for common operations. Since this is the last major piece of functionality for variables, I'll review and refactor some parts to simplify the organization and increase reusability. Colocating hooks and query keys will be a part of that refactor.

Related to #15512