userEvent.type not typing into Material UI DatePicker if it has focus

Reproduction example

https://codesandbox.io/p/sandbox/userevent-type-material-ui-datepicker-bug-px38kj

Prerequisites

1. Be on laptop/desktop such that the desktop variant of the DatePicker Component will be rendered. (Typing is not allowed in the mobile variant).
2. Have dependencies installed as specified in the provided codesandbox
3. Have a react component that renders the Material UI DatePicker Component
4. Have a test that uses userEvent.type to type into the DatePicker Component

Expected behavior

When the DatePicker component has focus before userEvent.type is called, then typing should occur and the field value should change accordingly.

Actual behavior

When the DatePicker component has focus before userEvent.type is called, then typing seems not to occur because the value of the field does not change.

User-event version

14.1.1

Environment

See package.json of codesandbox

Additional context

Example tests are provided in App.test.jsx in the codesandbox

Open the linked CodeSandbox and inspect App.test.jsx, then reproduce the focused Material UI DatePicker case with userEvent.type. Trace why the field value does not change and verify that typing works when the DatePicker already has focus without breaking the mobile-variant behavior described in the issue.