It seems tough to maintain standard Braille size with a tag that would hold up after numerous washings but not be itchy and bothersome when it contacts skin. It would also be large.

One option would be to have a small tag with a unique identifier of just a few characters (e.g. X2Q), and then have washing instructions with the same identifier on a separate hard copy sheet, and/or as a PDF, and/or as a web page.

You might be able to get a few characters embroidered on a tag that’s small enough to be sewn into a piece of clothing. To test this idea, you might try buying some embroidered Braille item for Etsy, and then if that works see what it would cost for quantity production from a shop that specializes in short run embroidery.

https://www.etsy.com/market/braille_embroidery

Some 2D codes such as QR codes might be printed or embroidered using a method that will hold up under numerous washings. This would be problematic, though, since the user would have to use a phone camera to point at the code, take a picture, etc.

WayAround has programmable clothing buttons that you can sew or pin to your items that are washer and dryer friendly. They’re inconspicuous and reusable. You do need to buy the wand thing that reads them, but it’s a very nice option. $1

Edit: it appears now the labels can be read by smartphones using their app!

There is an iOSApp by a Redditor: Laundry Lens

Not exactly what you are looking for but maybe it helps.

$1 is this kinda what youre looking for?

I cannot recall ever coming across braile labels for clothing.

Two Blind Brothers clothing has some kind of tag printed on some of it's clothing. I don't know what exactly it is, or what it's made of. It may be the metal tag you referred to.