fix(ai): la liste des fournisseurs de l'assistant suit la configuration (BUG-043)

Le picker lit /api/ai/status une seule fois, à sa construction, et le panneau
de l'assistant est un singleton monté pour toute la session : ajouter ou
supprimer une clé API dans la configuration du projet laissait la liste des
fournisseurs figée jusqu'à un rechargement de page.

- ai.js : nouveau refreshAIPickers() qui reconstruit chaque picker monté dans
  son emplacement .ai-picker-slot (constante PICKER_SLOT_CLASS) ; le slot est
  conservé même sans fournisseur configuré, donc le premier fournisseur ajouté
  s'y monte aussi ; une sélection persistée dont le fournisseur n'est plus
  configuré est purgée de obsigate_ai_picker (retour au défaut, plus de modèle
  fantôme dans le déclencheur).
- bookslm.js : l'emplacement .bookslm-picker-host porte la classe
  ai-picker-slot et reste dans la barre (replaceChildren au lieu de replaceWith).
- config.js : refreshAIPickers() après saveAIKeys() et deleteAIKey().
- tests : +4 tests JSDOM (ajout/retrait dans la barre, premier montage dans un
  slot vide, purge de la sélection orpheline, câblage save/delete).

Vérifié : tests frontend 66/66 (IA) + 9 suites JSDOM, validate-imports 36
modules, pytest 963 passed / 6 skipped, ruff 0, et contrôle navigateur
(Playwright) sur l'instance de test — ajout de nvidia visible sans rechargement,
retrait effectif + sélection réinitialisée.

tests/frontend/ai.test.mjs

@@ -1173,6 +1173,112 @@ async function main() {
     localStorage.clear();
   });
 
+  // ── 42c. BUG-043: the provider list follows the project AI configuration ──
+  const providerOptions = (root) =>
+    Array.from(root.querySelectorAll(".ai-picker-select option"))
+      .map((o) => o.value)
+      .filter(Boolean);
+
+  const providerStatusMock = (getProviders, models = ["deepseek-chat"]) => async (url) => {
+    const u = String(url);
+    if (u.includes("/api/ai/status")) {
+      return { ok: true, status: 200, json: async () => ({ configured: true, providers: getProviders() }) };
+    }
+    if (u.includes("/api/config/ai-models")) {
+      return { ok: true, status: 200, json: async () => ({ models, source: "api" }) };
+    }
+    return { ok: true, status: 200, json: async () => ({}) };
+  };
+
+  await test("assistant sidebar lists a provider added or removed in the project config", async () => {
+    localStorage.clear();
+    let providers = { deepseek: { available: true, model: "deepseek-chat" } };
+    globalThis.fetch = providerStatusMock(() => providers);
+
+    const b = new BooksLM();
+    b._panel = b._render();
+    document.body.appendChild(b._panel);
+    await sleep(30);
+    const host = b._panel.querySelector(".bookslm-picker-host");
+    assert.ok(host, "picker host lives in the toolbar");
+    assert.deepEqual(providerOptions(host), ["deepseek"], "only the configured provider is listed");
+
+    // Admin saves a second provider key in the project config.
+    providers = {
+      deepseek: { available: true, model: "deepseek-chat" },
+      nvidia: { available: true, model: "meta/llama-3.1-405b-instruct" },
+    };
+    await ai.refreshAIPickers();
+    await sleep(10);
+    assert.deepEqual(providerOptions(host), ["deepseek", "nvidia"], "added provider shows up without a reload");
+    assert.ok(host.querySelector(".ai-picker"), "picker rebuilt inside its host slot");
+    assert.equal(b._panel.querySelectorAll(".ai-picker").length, 1, "no duplicate picker mount");
+
+    // Admin deletes the key again.
+    providers = { deepseek: { available: true, model: "deepseek-chat" } };
+    await ai.refreshAIPickers();
+    await sleep(10);
+    assert.deepEqual(providerOptions(host), ["deepseek"], "removed provider disappears");
+
+    b._panel.remove();
+    localStorage.clear();
+  });
+
+  await test("refreshAIPickers mounts the first provider into an empty slot", async () => {
+    localStorage.clear();
+    let providers = {};
+    globalThis.fetch = providerStatusMock(() => providers);
+
+    const b = new BooksLM();
+    b._panel = b._render();
+    document.body.appendChild(b._panel);
+    await sleep(30);
+    const host = b._panel.querySelector(".bookslm-picker-host");
+    assert.equal(host.querySelector(".ai-picker"), null, "no picker without a configured provider");
+
+    providers = { deepseek: { available: true, model: "deepseek-chat" } };
+    await ai.refreshAIPickers();
+    await sleep(10);
+    assert.ok(host.querySelector(".ai-picker"), "picker mounted into the kept slot");
+    assert.deepEqual(providerOptions(host), ["deepseek"]);
+
+    b._panel.remove();
+    localStorage.clear();
+  });
+
+  await test("a provider whose key was deleted is dropped from the stored selection", async () => {
+    localStorage.clear();
+    globalThis.fetch = providerStatusMock(() => ({ deepseek: { available: true } }));
+
+    localStorage.setItem(
+      "obsigate_ai_picker",
+      JSON.stringify({ provider: "nvidia", model: "meta/llama-3.1-405b-instruct" })
+    );
+    const slot = document.createElement("span");
+    slot.className = "ai-picker-slot";
+    document.body.appendChild(slot);
+    slot.replaceChildren(await ai.buildAIPickerUI());
+    await sleep(20);
+
+    assert.equal(slot.querySelector(".ai-picker-select").value, "", "provider falls back to the default");
+    assert.equal(slot.querySelector(".ai-picker-model").value, "", "no stale model kept");
+    const stored = JSON.parse(localStorage.getItem("obsigate_ai_picker"));
+    assert.equal(stored.provider, null, "unconfigured provider cleared from storage");
+    assert.equal(stored.model, null, "its model cleared from storage");
+
+    slot.remove();
+    localStorage.clear();
+  });
+
+  await test("config save/delete rebuilds the assistant provider picker", async () => {
+    const { readFileSync } = await import("node:fs");
+    const src = readFileSync(path.join(JS_DIR, "config.js"), "utf-8");
+    const save = src.slice(src.indexOf("async function saveAIKeys()"), src.indexOf("async function deleteAIKey("));
+    const del = src.slice(src.indexOf("async function deleteAIKey("), src.indexOf("async function testAIKeys("));
+    assert.ok(save.includes("refreshAIPickers()"), "saving a provider key refreshes the picker");
+    assert.ok(del.includes("refreshAIPickers()"), "deleting a provider key refreshes the picker");
+  });
+
   // ── 42b. Assistant activity indicator (#82) ──
   await test("activity indicator reflects the request workflow", () => {
     const b = new BooksLM();