[mongodb/en] Fix logical operator syntax errors in examples

[manprit-tiwari]

This PR fixes incorrect MongoDB logical operator examples in the documentation.

Changes made:

• Corrected $and, $or, and $nor syntax (added proper object wrapping {}).
• Fixed $not example to use field-level condition.
• Verified all queries run correctly in MongoDB shell.

These corrections improve accuracy and help new learners avoid confusion.

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Checklist

• I solemnly swear that this is all original content of which I am the original author
• Pull request title is prepended with [mongodb/en]
• Pull request touches only one file (mongodb.md)
• Content changes are aimed at intermediate to experienced programmers
• YAML Frontmatter formatting verified