fix(agent): save conversations to DB, fix Test button hang, wire hasNext/search

## Root cause: _save_conversation() dead code + missing message persistence

### Backend: Conversation persistence (3 critical bugs)
- **app.py**: Replaced early  with  so _save_conversation() executes
  after successful stream — was dead code on normal path
- **app.py**: Added _save_conversation call in HITL resume path (confirm/deny)
- **app.py**: Added broad  that saves conversation (at least user
  message) before re-raising on LLM errors (APIConnectionError etc.)
- **app.py**: _save_conversation now passes user_id from JWT (not hardcoded UUID)
  and includes messages[] in payload
- **agent_conversations.py**: save_conversation endpoint now processes body.messages
  and creates AgentMessage records (idempotent by msg id)

### Frontend: Agent chat sidebar wiring
- AgentChatModel.svelte.ts: added public  derived getter
- AgentChatModel.svelte.ts: added  method
- agent/+page.svelte: wired hasNext={model.conversationsHasNext} (was hardcoded false)
- agent/+page.svelte: wired onsearch to model.searchConversations (was no-op)

### Frontend: LLM Provider Test button hang fix
- ProviderConfig.svelte: resetForm/handleEdit now reset isTesting=false, isProbing=false
- ProviderConfig.svelte: Cancel button calls abortPendingRequests()
- ProviderConfig.svelte: Added AbortController lifecycle — cancels in-flight test/fetch
  requests on modal close or provider switch, preventing stale disabled buttons
- provider_config.integration.test.ts: added 6 abort/reset invariant tests

backend/src/api/routes/agent_conversations.py

@@ -2,12 +2,14 @@
 # #region AgentChat.Api.Conversations [C:3] [TYPE Module] [SEMANTICS agent-chat,api,rest]
 # @defgroup AgentChat REST routes for conversation lifecycle.
 
+from datetime import datetime
+
 from fastapi import APIRouter, Depends, HTTPException, Query
 from sqlalchemy.orm import Session
 
 from ...core.database import get_db
 from ...dependencies import get_current_user
-from src.models.agent import AgentConversation
+from src.models.agent import AgentConversation, AgentMessage
 from src.schemas.agent import (
     ConversationItem,
     ConversationListResponse,
@@ -57,12 +59,10 @@ async def list_conversations(
 
 # #region AgentChat.Api.SaveConversation [C:3] [TYPE Function] [SEMANTICS agent-chat,api,save]
 # @ingroup AgentChat
-# @BRIEF POST /api/assistant/conversations/save — create or update conversation + messages.
+# @BRIEF POST /api/agent/conversations/save — create or update conversation + messages.
 # @PRE Service JWT with role=agent authenticates the Gradio container.
-# @POST Conversation saved (upsert by conversation_id). Existing messages appended.
+# @POST Conversation saved (upsert by conversation_id). Messages appended.
 # @SIDE_EFFECT Writes to AgentConversation and AgentMessage tables.
-from src.schemas.agent import SaveConversationRequest
-from datetime import datetime
 
 @agent_router.post("/conversations/save")
 async def save_conversation(
@@ -86,6 +86,30 @@ async def save_conversation(
     conv.updated_at = datetime.utcnow()
     if body.title:
         conv.title = body.title
+
+    # Save messages from payload
+    if body.messages:
+        for msg_data in body.messages:
+            msg_id = msg_data.get("id", "")
+            if not msg_id:
+                continue
+            # Check if message already exists (idempotent)
+            existing = db.query(AgentMessage).filter(
+                AgentMessage.id == msg_id,
+            ).first()
+            if not existing:
+                msg = AgentMessage(
+                    id=msg_id,
+                    conversation_id=body.conversation_id,
+                    role=msg_data.get("role", "user"),
+                    text=msg_data.get("text", ""),
+                    tool_calls=msg_data.get("tool_calls"),
+                    attachments=msg_data.get("attachments"),
+                    created_at=datetime.utcnow(),
+                )
+                db.add(msg)
+        db.flush()
+
     db.commit()
     return {"saved": True, "conversation_id": body.conversation_id}
 # #endregion AgentChat.Api.SaveConversation