I did some testing, and it seems that tags that I add to the page/document are not synced over to Readwise after being added, tags for individual highlights are however, highlighted. 
Perhaps this is a limitation of Readwise’s API?
That’s indeed a limitation of the readwise integration. Readwise only takes highlights, not saved pages last time I checked. But maybe they improved their API to also do that!
Readwise appears to support document-level tags - unclear is this extends to the API, but for downstream Roam Research integration this is a bit missing piece for me