### 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
hbc_button_replace->add_child(replace_all);
	replace_all->set_text(TTR("Replace All"));
	replace_all->connect("pressed", callable_mp(this, &FindReplaceBar::_replace_all));
	selection_only = memnew(CheckBox);
	hbc_option_replace->add_child(selection_only);
	selection_only->set_text(TTR("Selection Only"));
	selection_only->set_focus_mode(FOCUS_NONE);
	selection_only->connect("toggled", callable_mp(this, &FindReplaceBar::_search_options_changed));
	hide_button = memnew(TextureButton);
	add_child(hide_button);
	hide_button->set_focus_mode(FOCUS_NONE);
	hide_button->connect("pressed", callable_mp(this, &FindReplaceBar::_hide_bar));
	hide_button->set_v_size_flags(SIZE_SHRINK_CENTER);
}
void CodeTextEditor::input(const Ref<InputEvent> &event) {
	ERR_FAIL_COND(event.is_null());
	const Ref<InputEventKey> key_event = event;
	if (!key_event.is_valid()) {
		return;
	}
	if (!key_event->is_pressed()) {
		return;
	}
	if (!text_editor->has_focus()) {
		if ((find_replace_bar != nullptr && find_replace_bar->is_visible()) && (find_replace_bar->has_focus() || find_replace_bar->is_ancestor_of(get_viewport()->gui_get_focus_owner()))) {
			if (ED_IS_SHORTCUT("script_text_editor/find_next", key_event)) {
				find_replace_bar->search_next();
				accept_event();
				return;
			}