We have a 500 error on /api/lia/inbound:

"Error processing inbound message: could not determine data type of parameter $6"

This comes from the final UPDATE dp_conversations in app/lia_inbound.py. We need to fix the asyncpg type inference by casting the text parameters explicitly.

────────────────────────
TASK – Fix UPDATE dp_conversations parameter types

1. Open app/lia_inbound.py and find the UPDATE dp_conversations statement near the end of process_inbound_message. It currently looks roughly like:

    await conn.execute(
        """
        UPDATE dp_conversations
        SET stage = $1,
            status = $2,
            soft_no_count = $3,
            confusion_count = $4,
            needs_human_review = $5,
            escalation_reason = $6,
            escalation_at = CASE WHEN $6 IS NOT NULL THEN NOW() ELSE escalation_at END,
            appointment_status = $7,
            defer_until = $8,
            defer_reason = $9,
            updated_at = NOW()
        WHERE conversation_id = $10
        """,
        active_stage,
        status,
        new_soft_no_count,
        new_confusion_count,
        new_needs_human_review,
        escalation_reason,
        new_appointment_status,
        defer_until,
        defer_reason,
        conversation_id,
    )

2. Replace that SQL with this version, keeping the Python arguments EXACTLY the same:

    await conn.execute(
        """
        UPDATE dp_conversations
        SET stage = $1,
            status = $2,
            soft_no_count = $3,
            confusion_count = $4,
            needs_human_review = $5,
            escalation_reason = $6::text,
            escalation_at = CASE WHEN $6 IS NOT NULL THEN NOW() ELSE escalation_at END,
            appointment_status = $7,
            defer_until = $8,
            defer_reason = $9::text,
            updated_at = NOW()
        WHERE conversation_id = $10
        """,
        active_stage,           -- $1
        status,                 -- $2
        new_soft_no_count,      -- $3
        new_confusion_count,    -- $4
        new_needs_human_review, -- $5
        escalation_reason,      -- $6 (now cast to ::text above)
        new_appointment_status, -- $7
        defer_until,            -- $8
        defer_reason,           -- $9 (now cast to ::text above)
        conversation_id,        -- $10
    )

The only change is adding ::text on escalation_reason and defer_reason in the SQL.

3. Restart the server after the change.

────────────────────────
TEST

Re-run this inbound test:

POST /api/lia/inbound
x-api-key: lia_renewal_2025_super_secret_1

Body:

{
  "from_number": "+447700900001",
  "body": "Hi, could I pop in on Saturday morning to have a look at options?",
  "channel": "whatsapp",
  "conversation_id": null,
  "payments_remaining": 9
}

Expected:

- HTTP 200
- JSON body with LiaReply fields:
  - conversation_id
  - reply
  - mode
  - status
  - stage
  - defer_until (likely null)
- No "could not determine data type of parameter $6" error in logs.
- dp_conversations updated/created, and 2 dp_messages rows for this conversation (customer inbound + lia outbound).

────────────────────────
WHEN DONE

Reply with:
- The final UPDATE dp_conversations snippet you used.
- A sample of the 200 OK JSON response for the test payload (you can anonymise the reply text).