Do people know this usage in the states?

Busted in the US

We would probably say “busted” in this context but yes We would say “a business went bust” (or bankrupt)

It sounds weird. I would say "My watch is busted" as an American.

The example sentence would use busted in the US but the word is used. Calling something that was a failure "a bust" is also possible.

"busted" for that usage but "go bust" can be a synonym for "go bankrupt"

Busted meaning broken is commonly used, busted as in ugly is also used, but I'm not sure how common.

“The company went bust.” Yes You’d never say watch went bust in North America. If you broke your watch you’d say “The watch is busted.”

Also.... I'll bust your lip. She has a large bust

We recognize it, but typically only ever use it in the past tense to describe something that's broken. That, or if something's "a bust," would mean it's a failure. That's kind of old-timey sounding, though.

Not quite. In American English the verb bust means break, but we'd use past tense to form the adjective. We would say my watch is busted. Bust can also be an adjective in American English, but it means bankrupt. It's strangely related: to go bust is to go broke. The local bakery went bust.

In the US, "bust" / "busting" is slang for the thing that usually happens at the end of sex. For all partners, if it's any good: the term is not male-specific, unless further qualification is added. This seems to be relatively new. I don't remember hearing it used like that before the 2000s. "Busted" is slang for "got caught / got in trouble" as well as "broken." This has been so for many decades.

Yep. Bust or busted. Use it often. We also use it to describe peoples faces…not attractive people…it’s an insult. Or if you’re in a fight. Did you see Devon? His face is BUSTED! WTH man! Who did that to him?!

In Canada we would say something is 'busted' to mean broken. If you were to say something is 'bust' you would typically be describing financial diffuculty, or bankruptcy. "Did you hear? That cafe down on the corner went bust."

In England, bust would only really be used in that context in some dialects.

Bust just reminds me of boob's or a statue

The word is from the US, it's been loaned into British English as a doublet of "burst". "Bust" originates as a non-rhotic variation of "burst" in US English, whereas British English kept the "burst" spelling, but it gradually moved to a different vowel (/ɜː/). It's since taken on a distinct meaning. Similar situations can be found with cuss/curse and ass/arse.

as an american i would be asking where your watch is getting bussed to jk. but i don't think i've ever heard that usage

In the US we’d say “busted.”

As others have said, an American would much more commonly say busted. But I’ve heard this use in the South.