The rating feature is not available on communication sites, it is by default.
You can use PowerShell cmdlets to activate it, detailed information, you can refer to the article.
In addition, there is a user voice about this feature, you can vote it.
Reset the entire search index? No. Reindex a specific site via the button in site settings? Shouldn't cause any issues.
Also, check the site setting: "allow this site to appear in search results". And, it wouldn't hurt to verify with IT that the account that is used for the crawl has access to the site.