Send Feedback & Bug Reports to the Google Sites Team
Help Google Sites Improve by Submitting Feedback
On your Google Site, in editing mode, use the three-dot menu in the top right and select "Help Sites Improve" to submit written and screenshot feedback. Google will consider this feedback as a contribution to request top features to possible include in future patches / updates to the platform. FYI, Google does not respond to the feedback you send.
Most Requested Features for Google Sites
XML Sitemap submission support for Google Search to aid in thorough indexing of large sites
More supported image formats for lower site loads times with improved image quality
Blogging Support features like subpage listings, archives, article / post creation
Page level permissions to lock in viewers or editors for certain pages
Code Inject for Google Tag Manager and other custom code to embed in <head> section.
How to Send in Report & Screenshots
Enter the Google Site in edit mode
Go to the top right settings toolbar and select the 3 Dot Menu
Select Help Sites improve
Write a concise report, attach a screenshot, highlight screenshot portions (or hide them)
Allow for notification updates