The main search bar should have options to search within notes/annotations.
The advanced search should also the ability to filter by a particular tag (or multiple tags) that the user selects.
The search bar only shows common search terms that people use. You can search your notes using the "notes" keyword and any annotations by using the "highlighted_text" keyword. To search for multiple tags simply add the AND keyword. So if you have a tag for Elephant and a tag for Shark you can use the following query:
tag:Elephant AND tag:Shark
To see all you can do with search we highly recommend reading the following knowledge base article: Advanced Searching Syntax