Yes, this is a pain. According to this page it is not possible at the moment:
At the moment, you can show multi-reference field values only on a Collection page, and not within a Collection list. Support for nested Collection lists is planned. Vote for and subscribe to status updates of this feature request.
I’m wondering if you can solve this by using custom coding (jQuery), adding invisible collection list with the tags and somehow make the relation, but I doubt that this approach will succeed.
You will probably end up adding the tags in a separate text field as well, besides the multi-reference field. Maybe you can automate this process with Zapier, but I’m not sure if you can trigger a Webflow event into another Webflow event (when project item = published, update the extra tag text field with multi-reference tag input)…
Sorry for my thinking out load method as a reply. I’m curious though how this can be solved.