### 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
if (replace_text->has_focus() || search_text->has_focus()) {
		text_editor->grab_focus();
	}
	text_editor->set_search_text("");
	result_line = -1;
	result_col = -1;
	hide();
}
void FindReplaceBar::_show_search(bool p_focus_replace, bool p_show_only) {
	show();
	if (p_show_only) {
		return;
	}
	if (p_focus_replace) {
		search_text->deselect();
		replace_text->call_deferred(SNAME("grab_focus"));
	} else {
		replace_text->deselect();
		search_text->call_deferred(SNAME("grab_focus"));
	}
	if (text_editor->has_selection(0) && !is_selection_only()) {
		search_text->set_text(text_editor->get_selected_text(0));
		result_line = text_editor->get_selection_from_line();
		result_col = text_editor->get_selection_from_column();
	}
	if (!get_search_text().is_empty()) {
		if (p_focus_replace) {