What kind of figurative language is she was attired in deep mourning and excited in my bosom a feeling of mingled respect

The figurative language used is a metaphor. She was attired in deep mourning, a direct comparison to a feeling. It did not use "like" or "as" otherwise it would have been a simile

This is an example of a metaphor; a metaphor is a comparison between to things that don’t seem alike. In this case attired (a synonym of dressed) is used to compare the state of visible deep mourning of the woman the sentence is talking about, with the act of wearing the mourning, and of course, you can’t wear a feeling. The metaphor is used to highlight the fact that her mourning was so deep that was actually visible, like a dress.