How can I save a tag value in an entry in Craft 3
The trick here is that Tags are also elements, so you'll need to save them or look them up to assign them. Something like this:

    public function createOrGetTag($keyword, $groupId) {
        $tagQuery = new TagQuery(Tag::class);
        $tagQuery-&gt;groupId = $groupId;
        $tagQuery-&gt;title = $keyword;
        $tag = $tagQuery-&gt;one();

        if (!$tag) {
            $tag = new Tag();
            $tag-&gt;groupId = $groupId;
            $tag-&gt;title = $keyword;
            Craft::$app-&gt;elements-&gt;saveElement($tag);
        }

        return $tag;
    }


And then in your field setting, you'd do something like this:

$product-&gt;businessTag-&gt;id[] = $tag-&gt;id;