feat(auto): sticky route binding — plan the auto route once per session, not once per turn

[Hmbown]

Problem

The auto model router re-resolves on every user message: plan_turn_route (crates/tui/src/turn_route_plan.rs:143) runs the classifier (:146-166) per turn, and [auto] cross_provider (#4411) allows hopping providers turn-to-turn.

Every provider/model change forces a declared prefix-cache re-pin (crates/tui/src/core/engine.rs:7341-7374) — a guaranteed full cache miss on the next turn. With cache reads priced far below fresh input on every major provider, a per-turn auto route that switches models can cost more than the cheap model saves. Auto routing must be session-sticky: route once, stay bound.

Change

1. crates/tui/src/turn_route_plan.rs:143 — consult the session binding first. If bound and the binding still revalidates against ModelInventory (crates/tui/src/model_inventory.rs:77 — credential present, provider runnable, readiness), skip the classifier entirely and resolve the bound provider+model.
2. crates/tui/src/session_manager.rs:935 — promote SavedSession.last_auto_route (today: write-only provenance, set at tui/ui/event_loop.rs:2584 / dispatch.rs:933) to a load-bearing binding read at plan time. Already Option with serde defaults, so migration-safe.
3. Rebind only on: binding fails revalidation, the bound route errors at dispatch (client.rs:1421 / route/resolver.rs:218 re-resolution), or the user explicitly changes model/provider (already a declared re-pin).
4. [auto] cross_provider becomes a bind-time scope, not a per-turn permission: it widens the candidate set when the binding is created, not afterwards.

Already true, keep it that way

Transport retries and stream-resume never re-plan or switch provider (client.rs:3570, turn_loop.rs:1786-1941) — failure handling stays on the bound route.

Acceptance

• A session on model = "auto" makes at most one classifier call per binding; subsequent turns show routing_source: StickyBinding (feat(auto): receipts — record route bindings, rebinds, and sticky vs fresh routing source #6253).
• No prefix-cache re-pin occurs between turns that stay on the binding (verify via PrefixStabilityManager drift attribution, crates/core/src/prefix_cache.rs).
• Removing the bound provider credential and resuming the session triggers exactly one rebind, receipted.
• Explicit user model change busts the binding deliberately and is recorded as such.