Fix prototypes losing inherited data when a partial changes their parent

[Mackamuir]

This has been beating my ass for the last 2 weeks.

Issue

If a partial changes a protos parent:, it loses everything it should have inherited from further up the chain. It only keeps
what its new parent declares directly.

Example

# base.yml
- type: entity
  id: BaseItem
  abstract: true
  components:
  - type: Sprite
    sprite: Objects/Tools/tools.rsi

- type: entity
  parent: BaseItem
  id: BaseTool
  abstract: true
  components:
  - type: Item

- type: entity
  parent: BaseItem
  id: Wrench
  components:
  - type: Sprite
    layers:
    - state: wrench

# partial.yml
- type: !PartialOnly entity
  id: Wrench
  parent: !Clear BaseTool

What should happen:
Wrench gets Item from Basetool, and keeps the sprite path from BaseItem.

What currently happens:
Wrench gets Item but Sprite only gets layers and no sprite path, since BaseItem get's skipped, leading to the error:
Layer has no RSI to load states from. Cannot use 'state' property.

tldr: MultiRootInheritanceGraph.Add set the protos new parent list, but never told the old parents their child was gone, causing a stale edge that resolves the child too early, against a parent that hasn't been built yet.

Fix

Add now detaches the node from its old parents before wiring up the new ones, and assigns _parents[id] once rather than inside the loop.