The default Mastodon search only returns results for posts that have federated with your server and include a hashtag. Mastodon supports ElasticSearch/Full-text search. When enabled, users on a Mastodon server can search posts related to themselves. Examples:

• Posts they published
• Posts they favourited
• Posts where they were mentioned
• Their direct messages

This can be handy but requires a significant amount of extra server resources, so this feature is optional. On Masto.host ElasticSearch is available as a paid add-on.

Mastodon “does not allow searching for arbitrary strings in the entire database“. This means there is no option to search all posts on your server, whether you use the add-on or not.