docs(routing): LKGP sticks at provider level — align copy with routerStrategy contract (#11555)

Validated in a combined 4-PR batch worktree off release/v3.8.51 tip. Also removed a leftover changelog placeholder duplicate (0000-lkgp-doc-provider-stickiness.md, byte-identical content to the correctly-numbered 11555- fragment minus the PR link) — pushed to this branch.
- Focused test: router-strategies.test.ts — part of batch's 60/60 node:test run
- typecheck:core, file-size, changelog-integrity, complexity, cognitive-complexity, check:docs-counts-sync — all OK
- Full-repo lint: 228 pre-existing dashboard react-hooks/* findings, unrelated to this diff

Thanks for the docs-accuracy follow-through — aligning the LKGP copy with what routerStrategy.ts actually does (provider-level, not target/model) closes a real gap between prose and behavior.

docs/guides/USER_GUIDE.md

@@ -827,7 +827,7 @@ Configure via **Dashboard → Settings → Routing**. The dashboard exposes the
 - `p2c` (Power of Two Choices)
 - `least-used` and `cost-optimized`
 - `auto` — score-driven across all candidates
-- `lkgp` (Last Known Good Provider) — sticks to the last successful model per session
+- `lkgp` (Last Known Good Provider) — pins to the last successful provider, then falls back to rules
 - `context-optimized` — picks the model with the largest free context window
 - `context-relay` — chains long-context models for follow-up turns
 
@@ -1088,15 +1088,15 @@ Access via **Dashboard → Health**. Real-time system health overview with 6 car
 
 OmniRoute ships with a **score-driven auto-router** that picks the best model for each request across every connected provider — no combo to maintain. Just send the request with one of the `auto/*` prefixes and OmniRoute will assemble a virtual combo on the fly, scoring candidates on latency, cost, success rate, context fit, model fitness for the task, recent failures, quota, and circuit-breaker state.
 
-| Prefix         | Optimizes for                                                                 |
-| -------------- | ----------------------------------------------------------------------------- |
-| `auto`         | Balanced default (latency × cost × success rate)                              |
-| `auto/coding`  | Coding tasks: prefers Claude, GPT-5, GLM, Kimi, Qwen Coder, DeepSeek coders   |
-| `auto/cheap`   | Lowest $/token, accepts higher latency                                        |
-| `auto/fast`    | Lowest latency, ignores cost                                                  |
-| `auto/offline` | Local-only providers (Ollama, vLLM, llama.cpp) — useful for air-gapped setups |
-| `auto/smart`   | Reasoning quality first (Opus, GPT-5 xhigh, R1, GLM 5.1 reasoning)            |
-| `auto/lkgp`    | "Last Known Good Provider" — sticky to the most recently successful target    |
+| Prefix         | Optimizes for                                                                               |
+| -------------- | ------------------------------------------------------------------------------------------- |
+| `auto`         | Balanced default (latency × cost × success rate)                                            |
+| `auto/coding`  | Coding tasks: prefers Claude, GPT-5, GLM, Kimi, Qwen Coder, DeepSeek coders                 |
+| `auto/cheap`   | Lowest $/token, accepts higher latency                                                      |
+| `auto/fast`    | Lowest latency, ignores cost                                                                |
+| `auto/offline` | Local-only providers (Ollama, vLLM, llama.cpp) — useful for air-gapped setups               |
+| `auto/smart`   | Reasoning quality first (Opus, GPT-5 xhigh, R1, GLM 5.1 reasoning)                          |
+| `auto/lkgp`    | "Last Known Good Provider" — pins to the last successful provider, then falls back to rules |
 
 Example:
 

docs/routing/AUTO-COMBO.md

@@ -280,7 +280,7 @@ OmniRoute's combo engine supports **19 routing strategies** (declared in `src/sh
 | `headroom`          | Pick the target with the most remaining quota headroom                                                                                                                                    |
 | `strict-random`     | Random without deduplication of repeats                                                                                                                                                   |
 | `auto`              | Use Auto Combo scoring (15-factor) — **recommended**                                                                                                                                      |
-| `lkgp`              | Last-Known-Good Path (sticky route to last successful target)                                                                                                                             |
+| `lkgp`              | Last-Known-Good Path (pins to the last successful provider, then falls back to rules)                                                                                                     |
 | `context-optimized` | Pick target with best fit for current context size                                                                                                                                        |
 | `cache-optimized`   | Reorder targets by prompt-cache affinity — the connection likeliest to already hold this request's cached prefix is tried first (`open-sse/services/combo/promptCacheAffinity.ts`, #8008) |
 | `fusion` 🧬         | Fan out to a panel of models in parallel, then synthesize one answer via a judge (see below)                                                                                              |