“How does psychoanalysis help addiction?”

It probably doesn't. Sounds like a false promise unless the therapist is EXTREMELY skilled in specifically treating addictions. Decades ago, analysts claimed to be able to treat anything, but that didn't turn out well. Addiction is caused by a mixture of inheritance and a degree of emotional trauma. Addicts need ongoing emotional support and often a community to turn to.

See this link...
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5844159/
or
https://www.psychologytoday.com/us/blog/science-choice/201410/psychodynamic-way-understanding-addiction