Isn't the phrase "I'm sorry for your loss" grammatically incorrect?

I think it could mean: “I feel sorry for you, that you lost your brother”.
It’s not not so much an apologetic sentence as it is an empathic one.

The sentiment expressed outweighs all grammatical considerations. “I is sorry bout yo loss” is more than acceptable from someone who means it, because it is appreciated.

Since you mention it, yes. But the phrase itself is so proper it is standard English.

Sunrise and sunset are technically incorrect, too, from a scientific standpoint. But everybody assumes we know what the statement means, not that we are expressing something false.

English has many unspoken phrases in idiomatic usage, so it isn’t at all incorrect when you add the prepositional phrase, “...of your friend.”

The object is unstated but understood.

Language is about communication.

The grammatical “errors” throughout your informal text might make one wonder who’s winning the battle between prescriptivists and descriptivists.

When you’re grieving after someone dies…. do you get comfort from the phrase “I’m sorry for your loss” ?
Wouldn’t you rather hear: “Holy shit, that’s horrible. I’m really sorry.” ....?

I couldn’t care less about grammar at such a time. Sincere sympathy is appreciated though it is communicated in grunts.

It is elliptical, as is appropriate in a situation of great emotion.
It is why we yell ‘Help!” instead of “Would you kindly proffer me a hand, I am drowning”