Naming the Consistency Guarantee

A social app's post-creation flow: POST /posts writes to a primary Postgres database inside a SERIALIZABLE transaction that also increments the author's post count. Reads (GET /posts) are served from an asynchronously replicated read replica that can lag by up to 2 seconds.

1. Is the write path linearizable? Is it serializable? Justify both answers separately.
2. A user posts, then immediately refreshes their feed (routed to the replica) and does not see their new post. Which consistency property is violated, and is this a bug given the architecture as described?
3. What single architectural change would make the read path linearizable, and what does it cost?