Confessional poetry is a style of poetry, rather than a specific poetic form.  In other words, poets who write confessional poetry may choose a specific form or to make up their own.  Confessional poetry is a term that refers to the subject matter that poets choose to write about.

Here’s a good introduction to this type of poetry from poets.org:

https://www.poets.org/poetsorg/text/brief-guide-confessional-poetry