webui : store reasoning_content so it is sent back in subsequent requests (#21249)

tools/server/public/index.html

@@ -18,7 +18,7 @@
 		<div style="display: contents">
 			<script>
 				{
-					__sveltekit_1wqaxod = {
+					__sveltekit_10avopp = {
 						base: new URL('.', location).pathname.slice(0, -1)
 					};