Ah, it's hard/confusing to understand that documentation, even for me. As you can see from my previous post: value would be = title and key = id.
So I get now that a custom "value" could be set using "id=value|title", I didn't understand that at first.
So setting it that way, it still works fine for me.
$anredeField = $fields->options_anrede;
$opts = $anredeField->type->getOptions($anredeField);
$id = $opts->get("value=m")->id;
$page->options_anrede = $id;
...
The options config:
1=f|Frau
2=m|Herr
So again it's just assign the ID to the $page->youroptionsfield and save.