### 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_
import {
  deletePathInObject,
  getDisplayName,
  getDefaultComponentFilters,
  getInObject,
  getUID,
  renamePathInObject,
  setInObject,
  utfEncodeString,
} from 'react-devtools-shared/src/utils';
import {sessionStorageGetItem} from 'react-devtools-shared/src/storage';
import {
  cleanForBridge,
  copyToClipboard,
  copyWithDelete,
  copyWithRename,
  copyWithSet,
  getEffectDurations,
} from './utils';
import {
  __DEBUG__,
  PROFILING_FLAG_BASIC_SUPPORT,
  PROFILING_FLAG_TIMELINE_SUPPORT,
  SESSION_STORAGE_RELOAD_AND_PROFILE_KEY,
  SESSION_STORAGE_RECORD_CHANGE_DESCRIPTIONS_KEY,
  TREE_OPERATION_ADD,
  TREE_OPERATION_REMOVE,
  TREE_OPERATION_REMOVE_ROOT,
  TREE_OPERATION_REORDER_CHILDREN,
  TREE_OPERATION_SET_SUBTREE_MODE,