Please harden and finalise the /api/lia/nudge endpoint so it matches the safety and logging of /api/lia/outbound and /api/lia/inbound.

1) Locate the nudge implementation

- Open app/lia_nudge.py (or whichever file currently implements the nudge logic).
- Open app/main.py where the /api/lia/nudge endpoint is defined.

2) Conversation loading and safety checks

In the nudge processing function (e.g., process_nudge or similar), make sure it:

- Loads the conversation row from dp_conversations by conversation_id.
- If no conversation is found → raise an error that becomes HTTP 404 ("Conversation not found").
- If conversation.status = 'dnc' → raise a DNCBlockedError with message "Customer is DNC - no further contact allowed".
- If conversation.status = 'paused' → do NOT send a nudge; raise a NudgeBlockedError (or similar) that becomes HTTP 409 with message "Conversation is paused - no nudge sent".
- If conversation.defer_until is NOT NULL and defer_until > today → raise a NudgeBlockedError that becomes HTTP 409 with a message like "Conversation is deferred until YYYY-MM-DD - no nudge sent".

Reuse any existing DNCBlockedError class from lia_outbound if it already exists. If not, create one and keep it consistent.

3) Nudge generation and message logging

- Generate the nudge text using the existing rules / helper (whatever you already have for building a nudge message).
- Log the nudge to dp_messages using the same pattern as inbound/outbound:

  - sender = 'lia'
  - direction = 'outbound'
  - channel = conversation.channel
  - message_body = nudge_text
  - template_key = the template_key or mode used for the nudge (e.g., "NUDGE_12" or similar)
  - mode = a sensible string such as "NUDGE_12" or "NUDGE_GENERAL"

You can either call existing log_* helpers or insert into dp_messages directly if that’s the current pattern.

4) Update dp_conversations state

After sending/logging the nudge:

- Keep stage the same (nudges do not change stage).
- Keep status as 'active' unless you have a specific reason to change it.
- Always update updated_at = NOW().

If your nudge rules need to set a defer_until (for example, if you want to pause follow-ups for a few days after a nudge), you can set defer_until and defer_reason, but don’t invent new behaviour unless there is already a clear rule.

5) Response shape (LiaNudgeReply)

Make sure the nudge handler returns a JSON body with this shape:

{
  "conversation_id": "<uuid>",
  "status": "<active|paused|dnc>",
  "defer_until": "<YYYY-MM-DD or null>",
  "reply": "<nudge message text>",
  "stage": "<stage string such as '12' or '9'>"
}

This should be consistent with the existing LiaReply patterns.

6) Error handling in app/main.py

In app/main.py, update the /api/lia/nudge FastAPI endpoint to:

- Import and catch DNCBlockedError (and any new NudgeBlockedError you add).
- Map errors as follows:

  - DNCBlockedError → HTTP 409 with detail "Customer is DNC - no further contact allowed".
  - NudgeBlockedError (paused or deferred) → HTTP 409 with the message you set ("Conversation is paused - no nudge sent", or "Conversation is deferred until ...").
  - Conversation not found → HTTP 404.
  - Any obvious validation error → HTTP 400 with detail set to the error message.

7) Restart and test

Restart the server and run a couple of tests (you can use curl):

- Valid nudge for an active conversation_id → HTTP 200 with the JSON body described above.
- Nudge for a DNC conversation → HTTP 409 with DNC error.
- Nudge for a paused/deferred conversation → HTTP 409 with the paused/deferred message.
- Nudge for a non-existent conversation_id → HTTP 404.

Finally, please summarise the final /api/lia/nudge behaviour and show one example JSON response for a successful nudge in your reply.