How do I know if the Google Stars are properly embedded on the website?

To find out, use Google's Testing Tool: Rich Results Test - Google Search Console
Enter there your URL that you want to check.
This tool shows you errors, warnings and successfully included snippets, such as this (example is provenexpert.com):

Extract from Google's Testing Tool , in which the review snippet is highlighted

Important:

If your subpage already contains other snippets with structured rating data that are not the ProvenExpert Google Stars rich snippet or PRO Seal with rich snippet, the Google crawler may not recognize which snippet is the relevant one. In that case, we recommend you to remove the irrelevant rich snippet.