### 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_
L
      source: _debugSource || null,
      rootType,
      rendererPackageName: renderer.rendererPackageName,
      rendererVersion: renderer.version,
      plugins,
    };
  }
  let mostRecentlyInspectedElement: InspectedElement | null = null;
  let hasElementUpdatedSinceLastInspected: boolean = false;
  let currentlyInspectedPaths: Object = {};
  function isMostRecentlyInspectedElement(id: number): boolean {
    return (
      mostRecentlyInspectedElement !== null &&
      mostRecentlyInspectedElement.id === id
    );
  }
  function isMostRecentlyInspectedElementCurrent(id: number): boolean {
    return (
      isMostRecentlyInspectedElement(id) && !hasElementUpdatedSinceLastInspected
    );
  }
   Track the intersection of currently inspected paths,
   so that we can send their data along if the element is re-rendered.
  function mergeInspectedPaths(path: Array<string | number>) {
    let current = currentlyInspectedPaths;
    path.forEach(key => {
      if (!current[key]) {
        current[key] = {};
      }