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.

tests/unit/router-strategies.test.ts

@@ -262,6 +262,34 @@ test("lkgp — lkgpEnabled:false delegates to rules", () => {
   assert.equal(d.strategy, "rules");
 });
 
+test("lkgp — falls back to rules when the pool lacks the last known good provider", () => {
+  const pool = [cand({ provider: "x" })];
+  const context: RoutingContext = {
+    taskType: "default",
+    lastKnownGoodProvider: "y",
+  };
+  const d = getStrategy("lkgp").select(pool, context);
+  const expected = getStrategy("rules").select(pool, context);
+  assert.equal(d.strategy, expected.strategy);
+  assert.equal(d.provider, expected.provider);
+  assert.equal(d.model, expected.model);
+});
+
+test("lkgp — keeps the first candidate among several targets of the pinned provider", () => {
+  const pool = [
+    cand({ provider: "shared", model: "shared/m1", connectionId: "conn-1" }),
+    cand({ provider: "shared", model: "shared/m2", connectionId: "conn-2" }),
+  ];
+  const d = getStrategy("lkgp").select(pool, {
+    taskType: "default",
+    lastKnownGoodProvider: "shared",
+  });
+  assert.equal(d.provider, "shared");
+  assert.equal(d.model, "shared/m1");
+  assert.equal(d.connectionId, "conn-1");
+  assert.equal(d.candidatesConsidered, 1);
+});
+
 // ── selectWithStrategy + registry ─────────────────────────────────────────────
 test("selectWithStrategy — dispatches by name", () => {
   const pool = [