There is no interview process. You apply for the jobs posted online and if they're interested, they will email you confirmation of their interest and you will get an offer letter within a week or so. After that, and still never speaking to anyone outside of email..other than if you choose to call them, they will give you dates to begin your training. If multiple people apply, they base the order of who to hire first on if you were a previous or current USPS employee (priority), Military Service (if you are a vet.. automatically are placed at the top of the list), test scores (basic aptitude and customer service test), and date in which you applied.
There is a background check but other than felons.. it's nothing to worry about. And felons work at the USPS so it's not an automatic rejection.
There's little to no pre employment drug screenings since COVID 2020. Although some stations may vary.. it's highly suggested to again, not worry about it.