feat: persist chat read/unread state (server-backed)

[bjrump]

Context

Split out from #469 (finding 9). Today an "unread" state for chats exists client-side only: AppSidebar keeps an in-memory hasUnreadUpdate flag (manuallyUnreadChatIds / unreadChatIds) and renders a blue dot. There is no DB column, no API, no fetch — so the state is lost on reload and never syncs across sessions/devices.

#469 only adds an immediate cosmetic fix (the chat menu item now toggles between "Als ungelesen markieren" and "Als gelesen markieren"). This issue tracks the real feature.

Two concepts, one indicator

The current dot conflates two distinct ideas that a persisted model should keep separate:

• Manual unread — a user-asserted state ("mark as unread").
• New activity / background update — a system-detected change while the chat wasn't active.

Scope

• DB: add read-tracking to the chat model (e.g. last_read_at, or an explicit unread flag).
• API: endpoints to mark read/unread and to fetch unread state; include unread in chat summary/library contracts.
• Frontend: drive the sidebar indicator and the menu toggle from server state instead of in-memory refs; survive reload and sync across sessions.
• Decide whether manual-unread and new-activity are tracked separately or collapsed.

Notes

• Likely warrants an ADR (new persisted domain concept; the manual-vs-automatic distinction should be reflected in CONTEXT.md).
• Indicator visibility bug to keep in mind: the dot is currently suppressed on row hover / open menu (group-hover/chat-row:hidden).

[bjrump]

Edge cases to cover (surfaced during #469 review)

The minimal in-memory toggle shipped in #469 has known limitations that the persisted model here must resolve:

1. No persistence — unread state is lost on reload (session-entry + local-set only).
2. No-op without a live session entry — setHasUnreadUpdate early-returns when a chat has no entry (evicted by reclaimInertEntries, or after reload), so a server-backed store is needed for "mark as unread" to always stick.
3. Cross-section consistency — a chat shown in both the pinned and project lists tracks manual-unread partly in ProjectItem-local state, so marking it read/unread from different sections can leave a stale dot. A single shared (server-backed) source of truth fixes this.

These are why #469 keeps the toggle deliberately minimal.