"der Trauer" would be correct as an inflected form (genitive or dative singular), but that's not what you would list as a dictionary definition.
A good AI should be smart enough to know that if you ask for "German words with the article 'der'", you're most likely to want to be given a list of masculine nouns.
> Trauer is a feminine noun. Remember that, in German, both the spelling of the word and the article preceding the word can change depending on whether it is in the nominative, accusative, genitive, or dative case.[1]
[1]: https://www.collinsdictionary.com/dictionary/german-english/...