feat(client+home): single-instance family relations + DSC verified badge

- Family member dialog: disable Father / Mother / Spouse in the Relationship
  dropdown when one is already added to the client. Son, daughter, brother
  etc. stay unrestricted. Editing a member keeps its own current relation
  selectable. Hint added below the field.
- Home welcome banner: render a small green "DSC Verified" pill next to the
  username when GET /v1/dsc/me returns at least one ACTIVE certificate.
  Tooltip surfaces the masked serial. Silent when no DSC is mapped.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

src/app/home/home.component.scss

@@ -54,6 +54,10 @@ $accent: #0ea5e9;
     font-size: 20px;
     font-weight: 400;
     color: rgb(255 255 255 / 90%);
+    display: flex;
+    align-items: center;
+    flex-wrap: wrap;
+    gap: 6px;
 
     strong {
       font-weight: 700;
@@ -62,6 +66,70 @@ $accent: #0ea5e9;
   }
 }
 
+/* ── DSC Verified badge (welcome banner) ── */
+.dsc-badge {
+  display: inline-flex;
+  align-items: center;
+  gap: 8px;
+  margin-left: 10px;
+  padding: 4px 12px 4px 6px;
+  background: linear-gradient(135deg, rgb(34 197 94 / 18%) 0%, rgb(34 197 94 / 8%) 100%);
+  border: 1px solid rgb(74 222 128 / 35%);
+  border-radius: 999px;
+  font-size: 12px;
+  font-weight: 600;
+  letter-spacing: 0.02em;
+  color: #bbf7d0;
+  cursor: default;
+  transition:
+    transform 0.18s ease,
+    background 0.18s ease;
+
+  &:hover {
+    transform: translateY(-1px);
+    background: linear-gradient(135deg, rgb(34 197 94 / 28%) 0%, rgb(34 197 94 / 14%) 100%);
+  }
+
+  &__shield {
+    position: relative;
+    width: 26px;
+    height: 26px;
+    display: inline-flex;
+    align-items: center;
+    justify-content: center;
+    background: rgb(22 163 74 / 90%);
+    border-radius: 6px;
+    color: #fff;
+    font-size: 13px;
+    flex-shrink: 0;
+    box-shadow: 0 1px 3px rgb(15 118 50 / 35%);
+  }
+
+  &__check {
+    position: absolute;
+    right: -4px;
+    bottom: -4px;
+    width: 14px;
+    height: 14px;
+    background: #16a34a;
+    color: #fff;
+    border: 2px solid #1a5276; /* matches the banner's right edge so the ring blends in */
+    border-radius: 50%;
+    display: inline-flex;
+    align-items: center;
+    justify-content: center;
+    font-size: 8px;
+    line-height: 1;
+  }
+
+  &__label {
+    color: #ecfdf5;
+    text-transform: uppercase;
+    font-size: 10.5px;
+    letter-spacing: 0.06em;
+  }
+}
+
 .welcome-sub {
   margin: 4px 0 0;
   font-size: 12px;