PS: I am not having access to the comment, so adding it as an answer. Hope this is helpful.
Contact information is stored in the
xdbcollection database. You can check the data in the
[sc102_Xdb.Collection.Shard1].[xdb_collection].[ContactFacets]. If the contact is properly saved, you may find three records with
FacetKeysuch as Emails, ListSubscriptions (contains subscribed contact list details), and Personal (contains personal information).
You can also checkout the answer to the similar question for Sitecore 9 here: contact added manually not appeared in contact list in list manager sitecore 10.2 and see https://doc.sitecore.com/xp/en/developers/102/sitecore-experience-platform/rebuild-the-xdb-index-in-solr.html for more information on rebuilding the