Why does Free Tier instance not appear on the used Free Tier tab?

Hello.

It will take some time for it to be reflected in "billing and cost management".
It may take 24 hours, so I think it will be reflected tomorrow.
https://docs.aws.amazon.com/awsaccountbilling/latest/aboutv2/view-billing-dashboard.html

The data on this page comes from AWS Cost Explorer. If you haven’t used Cost Explorer before, it’s automatically enabled for you once you visit this page. It can take up to 24 hours for your data to appear on this page. When available, your data will be refreshed at least once every 24 hours. The Cost Explorer data on the home page is tailored for analytical purposes. This means the data can differ from your invoices and the Bills page due to differences in how data is grouped into AWS services; how discounts, credits, refunds, and taxes are displayed; differences in timing for the current month's estimated charges; and rounding.

Hello

it can take a little while for usage to be reflected accurately in your billing dashboard. The usage may not immediately appear in the " Free Tier" section, but as long as you've launched an instance that qualifies for the Free Tier, you should not be charged for it.

This questions relates the same already answered here, Please check https://repost.aws/questions/QUf8H0Iyf0QnuB3deLBHKgRQ/aws-free-tier-section-in-billing-dashboard-is-empty

This link also help you to configure alerts https://docs.aws.amazon.com/awsaccountbilling/latest/aboutv2/tracking-free-tier-usage.html