Native "select all" shortcut (Ctrl + A) does not work in Editor searchbar input in webComponents

Reproducible in vscode.dev or in VS Code Desktop?

• Not reproducible in vscode.dev or VS Code Desktop

Reproducible in the monaco editor playground?

• Not reproducible in the monaco editor playground

Monaco Editor Playground Link

https://microsoft.github.io/monaco-editor/playground.html?source=v0.37.1#example-creating-the-editor-web-component

Monaco Editor Playground Code

customElements.define(
	"code-view-monaco",
	class CodeViewMonaco extends HTMLElement {
		_monacoEditor;
		/** @type HTMLElement */
		_editor;

		constructor() {
			super();

			const shadowRoot = this.attachShadow({ mode: "open" });

			// Copy over editor styles
			const styles = document.querySelectorAll(
				"link[rel='stylesheet'][data-name^='vs/']"
			);
			for (const style of styles) {
				shadowRoot.appendChild(style.cloneNode(true));
			}

			const template = /** @type HTMLTemplateElement */ (
				document.getElementById("editor-template")
			);
			shadowRoot.appendChild(template.content.cloneNode(true));

			this._editor = shadowRoot.querySelector("#container");
			this._monacoEditor = monaco.editor.create(this._editor, {
				automaticLayout: true,
				language: "html",

				value: `<div>Hello World</div>`,
			});
		}
	}
);


HTML
<template id="editor-template">
	<div
		id="container"
		style="overflow: hidden; width: 100%; height: 100%; position: absolute"
	></div>
</template>

<code-view-monaco></code-view-monaco>

Reproduction Steps

-Press ctrl + F to open the search input in monaco editor
-Type anything in search input
-Press ctrl + A to select all in the search input (does nothing)

Actual (Problematic) Behavior

Native "select all" shortcut (Ctrl + A) does not work in Editor searchbar input in webComponents

Expected Behavior

Native "select all" shortcut (Ctrl + A) select all typed words in search input

Additional Context

No response

Start with the linked Monaco Editor Playground web-component example and reproduce the searchbar behavior after opening it with Ctrl+F. Trace the search input handling in the web component context, then verify that Ctrl+A selects all typed text in the search input without regressing ordinary editor search behavior.