feat(domain,application,infrastructure,backend,web-server,app-tauri,frontend): persistance et reprise des conversations de CLI custom par agent — index durable <projet>/.ideai/conversations/custom-index.json borné aux conversations non vides par agent (conversation_id logique, titre dérivé de la première invite, created/updated_at_ms), port CustomConversationIndex + adaptateur FsCustomConversationIndex, persistence des messages utilisateur et finals agent dans le log de conversation existant, DTO/commandes app-tauri et routes web-server pour lister/rouvrir, CustomAgentChatView: ouverture par défaut sur une nouvelle conversation, menu reprise d'une conversation passée ou nouvelle conversation, replay de l'historique sauvegardé (user+finals) à la réouverture, affichage normal des nouveaux messages après reprise, /clean ouvre une nouvelle conversation, aucune entrée créée si la conversation courante est vide, injection de l'historique dans le contexte agent différée au premier nouveau message après reprise — #363 (QA verte: git diff --check, cargo fmt --all -- --check, cargo tests ciblés infrastructure/application/web-server/app-tauri/backend, npm run typecheck, tests frontend ciblés et CustomAgentChatView, npm run build)

crates/domain/src/custom_conversation.rs

@@ -0,0 +1,43 @@
+//! Durable catalogue of user-facing custom CLI conversations.
+
+use async_trait::async_trait;
+use serde::{Deserialize, Serialize};
+
+use crate::ports::StoreError;
+use crate::{AgentId, ConversationId};
+
+/// One non-empty custom CLI conversation owned by an agent.
+#[derive(Debug, Clone, PartialEq, Eq, Serialize, Deserialize)]
+#[serde(rename_all = "camelCase")]
+pub struct CustomConversationEntry {
+    /// Stable logical conversation id used by log, handoff and provider-session stores.
+    pub conversation_id: ConversationId,
+    /// Agent that owns the conversation.
+    pub agent_id: AgentId,
+    /// Title derived from the first accepted user prompt.
+    pub title: String,
+    /// Creation timestamp in epoch milliseconds.
+    pub created_at_ms: u64,
+    /// Most recent persisted human/final activity in epoch milliseconds.
+    pub updated_at_ms: u64,
+}
+
+/// Project-scoped durable index for non-empty custom CLI conversations.
+#[async_trait]
+pub trait CustomConversationIndex: Send + Sync {
+    /// Lists conversations owned by `agent_id`, newest first and capped by `limit`.
+    async fn list(
+        &self,
+        agent_id: AgentId,
+        limit: usize,
+    ) -> Result<Vec<CustomConversationEntry>, StoreError>;
+
+    /// Finds an indexed conversation by logical id.
+    async fn get(
+        &self,
+        conversation_id: ConversationId,
+    ) -> Result<Option<CustomConversationEntry>, StoreError>;
+
+    /// Inserts the first non-empty prompt or updates the last-activity timestamp.
+    async fn upsert(&self, entry: CustomConversationEntry) -> Result<(), StoreError>;
+}

crates/domain/src/lib.rs

@@ -37,6 +37,7 @@ pub mod chat_attachment;
 pub mod chat_draft;
 pub mod conversation;
 pub mod conversation_log;
+pub mod custom_conversation;
 pub mod device;
 pub mod error;
 pub mod events;
@@ -177,6 +178,7 @@ pub use conversation_log::{
     TurnSlice, HANDOFF_SUMMARY_MAX_CHARS, MAX_ARCHIVE_SEGMENTS, PAGE_DEFAULT_LIMIT, PAGE_MAX_LIMIT,
     ROTATE_AFTER_BYTES, ROTATE_AFTER_TURNS,
 };
+pub use custom_conversation::{CustomConversationEntry, CustomConversationIndex};
 
 pub use device::{
     AuthenticatedDevice, DeviceError, DeviceId, DeviceName, PairedDevice, SessionTokenHash,