Add optional setting for showing "Model used:" information (#16337)

* feat: Add a setting to include model name used to generate the message

* feat: UI improvements

* feat: Save model info along with the database message entry creation

* chore: Build webui static output

tools/server/webui/src/lib/components/app/misc/ActionButton.svelte

@@ -34,7 +34,7 @@
 			{size}
 			{disabled}
 			{onclick}
-			class="h-6 w-6 p-0 {className}"
+			class="h-6 w-6 p-0 {className} flex"
 			aria-label={ariaLabel || tooltip}
 		>
 			{@const IconComponent = icon}