Audit and replace all usages of `app.graph`

Details: https://github.com/Comfy-Org/ComfyUI_frontend/pull/5372#issuecomment-3259238062

Audit and replace all usages of `app.graph` with a locator/gateway which allows much easier refactoring of the graph data model, along with making things more compatible with subgraphs (if subgraphs exist, `app.graph` may not be the desired graph that previous sites were expecting/desiring).

┆Issue is synchronized with this [Notion page](https://www.notion.so/Issue-5373-Audit-and-replace-all-usages-of-app-graph-2656d73d36508159acf7e85dd9a0f91c) by [Unito](https://www.unito.io)

Start with the details in the linked PR comment, then audit the frontend for every usage of `app.graph`. Define or locate the locator/gateway intended to replace it, and consider how it selects the desired graph when subgraphs exist; the work is done when the usages no longer rely directly on `app.graph`.

Written by the indexing model from the issue text.