You seem to know more about this than me. I have a family member who "invented" some electronics things. He hasn't done anything with the inventions (I'm pretty sure they're quackery).

But to ensure his patent, he mailed himself a sealed copy of the plans. He claims the postage date stamp will hold up in court if he ever needs it.

Is that a thing? Or is it just more tinfoil business? It's hard to tell with him.

It won't hold up in court, and given that the post-office will mail/deliver unsealed letters (which may then be sealed after the fact), will be viewed rather dimly.

Buy your family member a copy of:

https://www.goodreads.com/book/show/58734571-patent-it-yours...

Mailing yourself using registered mail is a very old tactic to establish a date for your documents using an official government entity, so this can be meaningful in court. However this may not provide the protection he needs. Copyright law differs from patent law and he should seek legal advice

Even if the date is verifiable, what would it even prove? If it's not public then I don't believe it can count as prior art to begin with.

The USmoved to first to file years ago. Whoever files first gets it, except if he publishes it publicly there is a 1-year inventor's grace period (it would not apply to a self mail or private mail to other people).

This is patent, not copyright.

Honestly I don't know whether that actually is a meaningful thing to do anymore; it may be with patents.

It certainly used to be a legal device people used.

Essentially it is low-budget notarisation. If your family member believes they have something which is timely and valuable, it might be better to seek out proper legal notarisation, though -- you'd consult a Notary Public:

https://en.wikipedia.org/wiki/Notary_public

presumably the intention is to prove the existence of the specific plans at a specific time?

I guess the modern version would be to sha256 the plans and shove it into a bitcoin transaction

good luck explaining that to a judge