### 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
emit_signal(SNAME("error"), p_label);
}
void FindReplaceBar::set_text_edit(CodeTextEditor *p_text_editor) {
	if (p_text_editor == base_text_editor) {
		return;
	}
	if (base_text_editor) {
		base_text_editor->remove_find_replace_bar();
		base_text_editor = nullptr;
		text_editor->disconnect("text_changed", callable_mp(this, &FindReplaceBar::_editor_text_changed));
		text_editor = nullptr;
	}
	if (!p_text_editor) {
		return;
	}
	results_count = -1;
	results_count_to_current = -1;
	needs_to_count_results = true;
	base_text_editor = p_text_editor;
	text_editor = base_text_editor->get_text_editor();
	text_editor->connect("text_changed", callable_mp(this, &FindReplaceBar::_editor_text_changed));
	_update_results_count();
	_update_matches_label();
}
void FindReplaceBar::_bind_methods() {
	ClassDB::bind_method("_search_current", &FindReplaceBar::search_current);
	ADD_SIGNAL(MethodInfo("search"));
	ADD_SIGNAL(MethodInfo("error"));
}
FindReplaceBar::FindReplaceBar() {