Reply to an existing Bluesky post, correctly setting both the 'root' and 'parent' strong references so the reply threads correctly even in deep reply chains.

Documented steps

1. Identify the post you are replying to (the 'parent'): you need both its at:// URI and its CID (a strong reference is exactly this uri+cid pair).
2. Determine the thread root: fetch the parent record with GET $PDSHOST/xrpc/com.atproto.repo.getRecord?repo=<did>&collection=app.bsky.feed.post&rkey=<rkey> (parse repo/collection/rkey out of the parent's at:// URI).
3. If the fetched parent record itself has a 'reply' field, its 'reply.root' is the thread's true root - fetch that root record too (same getRecord call, using the root's own uri/cid) and use its uri+cid as your reply's root.
4. If the fetched parent record has no 'reply' field, then the parent IS the root (it's a top-level post) - reuse the parent's uri+cid as both parent and root.
5. Build the reply field: {"root": {"uri": "<root at:// uri>", "cid": "<root cid>"}, "parent": {"uri": "<parent at:// uri>", "cid": "<parent cid>"}}.
6. Assemble the full post record: {"$type": "app.bsky.feed.post", "text": "your reply text", "createdAt": "<timestamp>", "reply": {...from step 5...}}, then createRecord with collection app.bsky.feed.post as usual.
7. For a reply directly to a top-level post, root and parent will be identical objects; for a reply nested several levels deep, root stays fixed at the original top-level post while parent changes to whichever comment you're directly answering.