I have seen a few sites now that have a help or feedback widget with a screenshot function. In my opinion this would be an excellent addition to the embedded chat widget both when starting a new chat or opening a ticket.
Often, when opening tickets from widgets like that, the exact issue can be seen on the page. An easy screenshot function would really help agents in quickly and precisely solving problems. The screenshot button could be placed just above the file upload option.
Here is an example of this on another products widget: https://support.freshdesk.com/support/solutions/articles/239273-setting-up-the-help-widget-to-embed-solution-articles-and-a-contact-form-in-your-website