MatAutocomplete panel does not close when the parent input changes focus programmatically.

### Is this a regression?

- [ ] Yes, this behavior used to work in the previous version

### The previous version in which this bug was not present was

_No response_

### Description

When adding host listener for keyboard navigation to other elements, the auto complete panel does not close.

### Reproduction

StackBlitz link: https://stackblitz.com/edit/angular-14-material-fbxecy?file=src%2Fauto-complete%2Fauto-complete.component.html
Steps to reproduce:
1. Click in the "Number" input.
2. Press Ctrl+DownArrow.
3. Observe that focus moves to the text area input without closing the panel.

### Expected Behavior

After the focus of the parent input moves to another element (either by click() or blur()), the panel should be closed.

### Actual Behavior

After moving focus from the parent input by using element.focus() the auto complete panel keeps visible until a click action takes place.

### Environment

- Angular: 14
- CDK/Material:
- Browser(s): Edge
- Operating System (e.g. Windows, macOS, Ubuntu): Windows

Open the linked StackBlitz reproduction and inspect src/auto-complete/auto-complete.component.html, then trace MatAutocomplete focus handling for programmatic focus changes. Reproduce the Ctrl+DownArrow flow and verify that moving focus with element.focus(), click(), or blur() closes the panel as expected.

Written by the indexing model from the issue text.