### Website or app

https://codesandbox.io/s/forwardref-context-change-did-not-render-lpdk4t?file=/src/index.js

### Repro steps

1. Goto https://lpdk4t.csb.app/
1. Start profiling
3. Enter "a" into the input
4. Stop profiling
![forwardRef-did-not-render](https://user-images.githubusercontent.com/12292047/164915101-f28f305a-2c51-4b89-8515-da073e5551c9.png)



### How often does this bug happen?

Every time

### DevTools package (automated)

_No response_

### DevTools version (automated)

4.24.3-46a98cff2

### Error message (automated)

_No response_

### Error call stack (automated)

_No response_

### Error component stack (automated)

_No response_

### GitHub query string (automated)

_No response_
instance.props,
              oldPath,
              newPath,
            );
            instance.forceUpdate();
          }
          break;
        case 'state':
          renamePathInObject(instance.state, oldPath, newPath);
          instance.forceUpdate();
          break;
      }
    }
  }
  function overrideValueAtPath(
    type: 'context' | 'hooks' | 'props' | 'state',
    id: number,
    hookID: ?number,
    path: Array<string | number>,
    value: any,
  ): void {
    const fiber = findCurrentFiberUsingSlowPathById(id);
    if (fiber !== null) {
      const instance = fiber.stateNode;
      switch (type) {
        case 'context':
           T
           t
           W
          path = path.slice(1);