More 516 fixes and TGUI improvements (#26617)

* more 516 fixes and tweaks

* cleaned build output

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Co-authored-by: Burzah <116982774+Burzah@users.noreply.github.com>

code/modules/client/client_procs.dm

@@ -269,7 +269,7 @@
 /client/New(TopicData)
 	// TODO: Remove with 516
 	if(byond_version >= 516) // Enable 516 compat browser storage mechanisms
-		winset(src, "", "browser-options=byondstorage")
+		winset(src, "", "browser-options=byondstorage,find")
 
 	var/tdata = TopicData //save this for later use
 	// Instantiate stat panel

code/modules/tgui/tgui_panel/tgui_panel_external.dm

@@ -34,6 +34,8 @@
 	// Force show the panel to see if there are any errors
 	winset(src, "output", "is-disabled=1&is-visible=0")
 	winset(src, "chat_panel", "is-disabled=0;is-visible=1")
+	if(byond_version >= 516)
+		winset(src, null, "browser-options=byondstorage,find")
 
 /client/verb/refresh_tgui()
 	set name = "Refresh TGUI"