Index: /trunk/src/wp-admin/css/dashboard.css
===================================================================
--- /trunk/src/wp-admin/css/dashboard.css	(revision 62942)
+++ /trunk/src/wp-admin/css/dashboard.css	(revision 62943)
@@ -725,9 +725,17 @@
 }
 
+#dashboard_right_now #wp-version-message {
+	display: flex;
+	flex-wrap: wrap;
+	align-items: center;
+	gap: 8px;
+}
+
+#dashboard_right_now #wp-version {
+	flex: 1;
+}
+
 #dashboard_right_now #wp-version-message .button {
-	float: right;
-	position: relative;
-	top: -5px;
-	margin-left: 5px;
+	margin-left: auto;
 }
 
Index: /trunk/src/wp-admin/includes/update.php
===================================================================
--- /trunk/src/wp-admin/includes/update.php	(revision 62942)
+++ /trunk/src/wp-admin/includes/update.php	(revision 62943)
@@ -363,19 +363,4 @@
 	}
 
-	$msg = '';
-
-	if ( current_user_can( 'update_core' ) ) {
-		$cur = get_preferred_from_update_core();
-
-		if ( isset( $cur->response ) && 'upgrade' === $cur->response ) {
-			$msg .= sprintf(
-				'<a href="%s" class="button" aria-describedby="wp-version">%s</a> ',
-				network_admin_url( 'update-core.php' ),
-				/* translators: %s: WordPress version number, or 'Latest' string. */
-				sprintf( __( 'Update to %s' ), $cur->current ? $cur->current : __( 'Latest' ) )
-			);
-		}
-	}
-
 	/* translators: 1: Version number, 2: Theme name. */
 	$content = __( 'WordPress %1$s running %2$s theme.' );
@@ -392,5 +377,18 @@
 	$content = apply_filters( 'update_right_now_text', $content );
 
-	$msg .= sprintf( '<span id="wp-version">' . $content . '</span>', get_bloginfo( 'version', 'display' ), $theme_name );
+	$msg = sprintf( '<span id="wp-version">' . $content . '</span>', get_bloginfo( 'version', 'display' ), $theme_name );
+
+	if ( current_user_can( 'update_core' ) ) {
+		$cur = get_preferred_from_update_core();
+
+		if ( isset( $cur->response ) && 'upgrade' === $cur->response ) {
+			$msg .= sprintf(
+				'<a href="%s" class="button" aria-describedby="wp-version">%s</a>',
+				network_admin_url( 'update-core.php' ),
+				/* translators: %s: WordPress version number, or 'Latest' string. */
+				sprintf( __( 'Update to %s' ), $cur->current ? $cur->current : __( 'Latest' ) )
+			);
+		}
+	}
 
 	echo "<p id='wp-version-message'>$msg</p>";