docsearch: Upgrade to v3 (#231)

See:
- https://docsearch.algolia.com/docs/DocSearch-v3
- https://docsearch.algolia.com/docs/migrating-from-v2

src/resources/css/common.css

@@ -82,29 +82,18 @@ header nav > a.current {
 	font-weight: bold;
 }
 
-/* Algolia search */
+/* Algolia DocSearch */
 #search {
-	border-radius: 5px;
-	border: 1px solid rgba(0, 0, 0, .2);
-	font-size: 14px;
-	padding: 8px;
-	background: none;
-	width: 200px;
-	max-width: 100%;
-	margin-right: 20px;
-	margin-top: 4px;
-	outline: none;
+	display: inline-block;
+	vertical-align: middle;
 }
-
-#search:focus {
-	background: #fff;
+.DocSearch-Container {
+	color: initial;
 }
-
-.algolia-autocomplete .ds-dropdown-menu {
-	width: 90%;
-	max-width: 800px;
+.DocSearch-Footer {
+	margin-top: 0;
 }
-/* End Algolia search */
+/* End Algolia DocSearch */
 
 header nav .new {
 	background-color: #ffe300;

src/resources/css/docs.css

@@ -918,13 +918,16 @@ td code {
 		color: black;
 	}
 
+	/* Algolia DocSearch */
 	#search {
-		background: rgb(28, 52, 79);
-		color: #bdd6f7;
-	}
-	#search:focus {
-		background: rgb(46, 70, 96);
+		--docsearch-searchbox-background: rgb(28, 52, 79);
+		--docsearch-searchbox-focus-background: rgb(28, 52, 79);
+		--docsearch-text-color: #bdd6f7;
+		--docsearch-muted-color: #96a9c4;
+		--docsearch-key-gradient: linear-gradient(-26.5deg, #060e17 0%, rgb(47, 62, 72) 100%);
+		--docsearch-key-shadow: inset 0 -2px 0 0 #4c4c56, inset 0 0 1px 1px rgb(70, 70, 70), 0 1px 2px 1px rgba(77, 79, 91, 0.4);
 	}
+	/* End Algolia DocSearch */
 
 	#paper1,
 	#paper2 {