feat: création de projet (nouveau dossier + session) & en-tête de session enrichi

- POST /api/v1/projects : crée <root>/<name> (mkdir non récursif, 409 si existant),
  git init optionnel, puis lance une session dedans. Anti-traversal sur le nom (core/project.ts).
- Web : NewProjectModal (racine préremplie scanRoots[0], case git init) + bouton dans SessionsListView.
- SessionContextBar : badge du groupe (cliquable) + repos couverts avec leur branche dans l'en-tête
  de session ; session simple = repo+branche déduits du cwd.
- 14 tests (unitaires + route).

packages/web/src/components/NewProjectModal.vue

@@ -0,0 +1,119 @@
+<template>
+  <div class="fixed inset-0 z-50 flex items-center justify-center bg-black/60 p-4" @click.self="emit('close')">
+    <div class="flex max-h-[90vh] w-full max-w-lg flex-col gap-3 overflow-y-auto rounded-lg border border-zinc-800 bg-zinc-900 p-4">
+      <header class="flex items-center gap-2">
+        <h2 class="font-semibold text-zinc-100">{{ t('project.title') }}</h2>
+        <button class="btn ml-auto text-xs" @click="emit('close')">{{ t('common.cancel') }}</button>
+      </header>
+      <p class="text-xs text-zinc-500">{{ t('project.intro') }}</p>
+
+      <form class="flex flex-col gap-3" @submit.prevent="onSubmit">
+        <label class="flex flex-col gap-1 text-xs text-zinc-400">
+          {{ t('project.nameLabel') }}
+          <input v-model="name" class="input font-mono" :placeholder="t('project.namePlaceholder')" required :disabled="creating" />
+        </label>
+
+        <label class="flex flex-col gap-1 text-xs text-zinc-400">
+          {{ t('project.rootLabel') }}
+          <input v-model="root" class="input font-mono" :placeholder="t('project.rootPlaceholder')" required :disabled="creating" />
+        </label>
+        <div>
+          <button type="button" class="btn text-xs" :disabled="creating" @click="showPicker = !showPicker">{{ t('fs.browse') }}</button>
+        </div>
+        <DirectoryPicker v-if="showPicker" mode="dir" :initial-path="root" @select="onPickRoot" @close="showPicker = false" />
+
+        <label class="flex items-center gap-2 text-xs text-zinc-300">
+          <input v-model="gitInit" type="checkbox" :disabled="creating" /> {{ t('project.gitInit') }}
+        </label>
+
+        <label class="flex flex-col gap-1 text-xs text-zinc-400">
+          {{ t('project.commandLabel') }}
+          <select v-model="command" class="input" :disabled="creating">
+            <option value="claude">claude</option>
+            <option value="bash">bash</option>
+          </select>
+        </label>
+
+        <p class="font-mono text-[11px] text-zinc-500">{{ previewPath }}</p>
+        <p v-if="errorMsg" class="text-xs text-red-400">{{ errorMsg }}</p>
+
+        <div class="flex items-center gap-2">
+          <button type="submit" class="btn-primary" :disabled="creating || name.trim() === '' || root.trim() === ''">
+            {{ creating ? t('project.creating') : t('project.create') }}
+          </button>
+        </div>
+      </form>
+    </div>
+  </div>
+</template>
+
+<script setup lang="ts">
+import { computed, onMounted, ref } from 'vue';
+import { useRouter } from 'vue-router';
+import { useI18n } from 'vue-i18n';
+import { useSessionsStore } from '../stores/sessions';
+import { useSettingsStore } from '../stores/settings';
+import { useToastsStore } from '../stores/toasts';
+import DirectoryPicker from './DirectoryPicker.vue';
+
+const emit = defineEmits<{ close: [] }>();
+
+const { t } = useI18n();
+const router = useRouter();
+const sessions = useSessionsStore();
+const settings = useSettingsStore();
+const toasts = useToastsStore();
+
+const name = ref('');
+// Racine par défaut : la 1ère racine de scan (réglage Découverte) ; modifiable via le picker.
+const root = ref('');
+const gitInit = ref(false);
+const command = ref<'claude' | 'bash'>('claude');
+const showPicker = ref(false);
+const creating = ref(false);
+const errorMsg = ref<string | null>(null);
+
+// Aperçu du chemin final (indicatif ; jointure naïve suffisante pour l'affichage).
+const previewPath = computed(() => {
+  const r = root.value.trim().replace(/\/+$/, '');
+  const n = name.value.trim();
+  return r && n ? `${r}/${n}` : '';
+});
+
+onMounted(async () => {
+  if (!settings.loaded) {
+    try {
+      await settings.fetch();
+    } catch {
+      /* le préremplissage de la racine est facultatif */
+    }
+  }
+  root.value = settings.scanRoots[0] ?? '';
+});
+
+function onPickRoot(path: string): void {
+  root.value = path;
+  showPicker.value = false;
+}
+
+async function onSubmit(): Promise<void> {
+  if (creating.value || name.value.trim() === '' || root.value.trim() === '') return;
+  creating.value = true;
+  errorMsg.value = null;
+  try {
+    const res = await sessions.createProject({
+      root: root.value.trim(),
+      name: name.value.trim(),
+      gitInit: gitInit.value,
+      command: command.value,
+    });
+    toasts.success(t('toast.projectCreated'));
+    emit('close');
+    await router.push({ name: 'session', params: { id: res.session.id } });
+  } catch (err) {
+    errorMsg.value = err instanceof Error ? err.message : String(err);
+  } finally {
+    creating.value = false;
+  }
+}
+</script>