### Godot version

v4.0.beta14.official

### System information

Windows 11 22H2

### Issue description

There's not much to it, simply noticed that if you have Find or Find+Replace opened in the Script Editor, the Multi-Caret functionality seems to stop working -- forcibly removing all other carets after the first character is typed. I'd expect the Multi-Caret to remain until unselected by clicking elsewhere.

The content of what's in "Find" doesn't matter, it happens regardless.

https://user-images.githubusercontent.com/8159582/214234069-cbcc1681-3f09-4b10-9a90-857cc91d41a7.mp4



### Steps to reproduce

1. Open the Find or Find+Replace tool in the Script Editor _(nothing has to be inputted)_
2. Add multiple mouse cursors with Ctrl+Alt+Click **OR** highlight something and then highlight additional duplicates with Ctrl+D _(or synonymous keyboard shortcuts depending on OS)_.
3. Start typing as if going to add or replace in all locations where the multi-caret is

### Minimal reproduction project

N/A
switch (p_what) {
		case NOTIFICATION_READY:
		case EditorSettings::NOTIFICATION_EDITOR_SETTINGS_CHANGED: {
			find_prev->set_icon(get_theme_icon(SNAME("MoveUp"), SNAME("EditorIcons")));
			find_next->set_icon(get_theme_icon(SNAME("MoveDown"), SNAME("EditorIcons")));
			hide_button->set_texture_normal(get_theme_icon(SNAME("Close"), SNAME("EditorIcons")));
			hide_button->set_texture_hover(get_theme_icon(SNAME("Close"), SNAME("EditorIcons")));
			hide_button->set_texture_pressed(get_theme_icon(SNAME("Close"), SNAME("EditorIcons")));
			hide_button->set_custom_minimum_size(hide_button->get_texture_normal()->get_size());
		} break;
		case NOTIFICATION_VISIBILITY_CHANGED: {
			set_process_unhandled_input(is_visible_in_tree());
		} break;
		case NOTIFICATION_THEME_CHANGED: {
			matches_label->add_theme_color_override("font_color", results_count > 0 ? get_theme_color(SNAME("font_color"), SNAME("Label")) : get_theme_color(SNAME("error_color"), SNAME("Editor")));
		} break;
		case NOTIFICATION_PREDELETE: {
			if (base_text_editor) {
				base_text_editor->remove_find_replace_bar();
				base_text_editor = nullptr;
			}
		} break;
	}
}
void FindReplaceBar::unhandled_input(const Ref<InputEvent> &p_event) {