website: unify and enhance styling of search boxes

Unify the coloring of the search boxes in the sidebar and the navigation bar.
Update the icon color to the secondary color to create an accent effect.

website/assets/scss/_variables_project.scss

@@ -32,4 +32,23 @@ $td-sidebar-tree-root-color: #222 !default;
   .td-arrow-down:before {
     border-color: $secondary transparent transparent transparent !important;
   }
+}
+
+.td-search__input {
+  color: var(--bs-body-color) !important;
+  border: 1px solid var(--bs-gray-400) !important;
+}
+
+.td-search__input:focus {
+  color: inherit !important;
+  border-color: var(--bs-body-bg) !important;
+  box-shadow: 0 0 0 2px var(--bs-primary) !important;
+}
+
+.td-search__input::placeholder {
+  color: var(--bs-gray) !important;
+}
+
+.td-search__icon {
+  color: $secondary !important;
 }