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It can take some time for Google to discover and index new backlinks to your site. Google's crawler needs to visit and index the pages containing the backlinks before they appear in the Google Search Console.

If your website has crawlability issues, Google's crawler may not be able to access and index the pages containing your backlinks.

Solution: Ensure that your website is properly structured, and there are no crawl errors. Use Google Search Console's 'Crawl' section to identify and fix any crawl issues. The same issue I was also faced when I make backlinks for my website and once I apply this strategy, my issue was resolved within few minutes.