You don’t tell anyone. This is more relevant for things that aren’t easily reverse engineered, such as recipes, high tech methods, software, etc.
In order to be granted a patent, the government requires that you explicitly detail how to create or perform whatever your patent is over in extreme detail so that anyone in the relevant industry can recreate it after the patent expires.
Patents expire after 20 years, but you have a guaranteed monopoly protected by the government.
Trade secrets grant no legal protection (sorta, it’s complicated). It’s literally just keeping things secret to prevent knockoffs. The trade off is that if someone reverse engineers your thing, you have no legally protected monopoly. So your advantage can last a few months (if reverse engineered) or well beyond the 20 years that would’ve been offered by a patent.
Some things are tightly regulated though, so it’s impossible to operate with secrets - think drug manufacturing.
USPS does not know the contents of the boxes delivered, unlike the pharmacies in your example.