### 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
is_errors_panel_opened = p_show;
	emit_signal(SNAME("show_errors_panel"), p_show);
}
void CodeTextEditor::_set_show_warnings_panel(bool p_show) {
	is_warnings_panel_opened = p_show;
	emit_signal(SNAME("show_warnings_panel"), p_show);
}
void CodeTextEditor::_toggle_scripts_pressed() {
	ScriptEditor::get_singleton()->toggle_scripts_panel();
	update_toggle_scripts_button();
}
void CodeTextEditor::_error_pressed(const Ref<InputEvent> &p_event) {
	Ref<InputEventMouseButton> mb = p_event;
	if (mb.is_valid() && mb->is_pressed() && mb->get_button_index() == MouseButton::LEFT) {
		goto_error();
	}
}
void CodeTextEditor::_update_status_bar_theme() {
	error_button->set_icon(get_theme_icon(SNAME("StatusError"), SNAME("EditorIcons")));
	error_button->add_theme_color_override("font_color", get_theme_color(SNAME("error_color"), SNAME("Editor")));
	error_button->add_theme_font_override("font", get_theme_font(SNAME("status_source"), SNAME("EditorFonts")));
	error_button->add_theme_font_size_override("font_size", get_theme_font_size(SNAME("status_source_size"), SNAME("EditorFonts")));
	warning_button->set_icon(get_theme_icon(SNAME("NodeWarning"), SNAME("EditorIcons")));
	warning_button->add_theme_color_override("font_color", get_theme_color(SNAME("warning_color"), SNAME("Editor")));
	warning_button->add_theme_font_override("font", get_theme_font(SNAME("status_source"), SNAME("EditorFonts")));
	warning_button->add_theme_font_size_override("font_size", get_theme_font_size(SNAME("status_source_size"), SNAME("EditorFonts")));
	line_and_col_txt->add_theme_font_override("font", get_theme_font(SNAME("status_source"), SNAME("EditorFonts")));
	line_and_col_txt->add_theme_font_size_override("font_size", get_theme_font_size(SNAME("status_source_size"), SNAME("EditorFonts")));
}
void CodeTextEditor::_notification(int p_what) {