That's not exactly the case here. You aren't blindly sending such information as a reply. The email, as shown in the initial post, includes a link that takes you to the Select Payment page.
I got the same type of email for the previous lawsuit. The link took the user to this page.
https://www.smartphoneperformancesettlement.com/
Once there, you clicked the link (now expired) to submit your claim form online. And yes, it asked for a bank routing and account number.
Still, only after investing it for possible fraud did I fill anything out. By the time a $96 payment (or whatever the actual amount was) appeared in our bank account months later, I had completely forgotten about it.