Match search component styles to the search bar

src/App.scss

@@ -665,6 +665,9 @@ option {
 }
 
 .alert {
+  display: inline-flex;
+  justify-content: center;
+  align-items: center;
   line-height: 1;
   margin: 0 0.5em;
   padding: 0.35em;

src/components/search/search.vue

@@ -176,10 +176,19 @@
     font-size: 1rem;
     padding: 0.5rem;
     box-sizing: border-box;
+    border-top-right-radius: 0;
+    border-bottom-right-radius: 0;
   }
 
   .search-button {
-    margin-left: 0.5em;
+    aspect-ratio: 1/1;
+    border-top-left-radius: 0;
+    border-bottom-left-radius: 0;
+    box-shadow: var(--inputShadow);
+
+    &:hover {
+      box-shadow: var(--buttonHoverShadow);
+    }
   }
 }
 
@@ -211,5 +220,4 @@
     color: var(--text, $fallback--text);
   }
 }
-
 </style>