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Search Console does not show all backlinks to your website, just a sample

First of all, I recommend you verify if the structured data markup is correct with this tool: https://validator.schema.org/

Then you can pass it through this one: https://search.google.com/test/rich-results to see if Google can show rich results.
Likewise, even if everything is fine, it is Google's decision to show or not the stars

Search Console does not show all backlinks to your website, just a sample