So I did a bit a bit of a deep dive for funsies and few people said they were interested in me sharing what I found, so I made a nice neat pictures and organized it all for you.
This data comes from multiple places- mostly Honey Hunter to keep it all uniform. I double checked across the Chinese Genshin Wiki and both English one (Fandom and HoyoWiki).
Please no reposting this time.

Need to Know:
The word 义兄弟 is "Sworn Brothers" with 义兄 being Sworn Older Brother and 义弟 Sworn Younger Brother.
A Sworn Brotherhood is a very close bond of friendship. 义 is quite literally 'of righteousness' and 兄弟 can mean either actual brothers or friends according to the grammar. When used as a singular word, it's always friends. (Example: "I am Caleb's 兄弟" is friends but "Caleb and I are 兄弟" is family.) It is very common to see the word 兄弟 in Genshin, from Itto especially, to symbolize groups and friends because of this.
So you can read 义兄弟 quite literally as "friends of righteousness" or Friends of Great Loyalty. Essentially, that is correct. It's just a super ultra close friendship with you and your closest people to always support each other in weal and woe. For better or worse.
So that being said, the words I were specifically looking for were '义兄", "义弟", and "Sworn Brother"
Since we already know Kaeya says both, but not the english version, he will not be included in this.
First up: Alley Flash

So in this case, the Hanzi says brothers. Like actual, blood related, real actual brothers. At least half, on their mother's side specifically. This EN translation is super strange and makes no sense.
Second up: A Cliff-Side Hero's Past

In this instance, the Hanzi says "My Brother of Iron". Pretty easy to figure out this was supposed to be Man of Steel or Brother of Arms. Sworn Brother is similar to that concept, but this is very backwards. Why the EN decided to switch this to Sworn, I have no idea. Not as weird as the first one, but it's strange.
In addition- they had the traveler respond "your friend" to it?
While this acknowledges that the meaning is still just friends, it's strange.
Third up: Haran Geppaku Futsu

Like I said in the image, this is the one and only instance in Genshin I've managed to find where Sworn Brother is translated as Sworn Brother in English. In the story, I find the fact they made it Sworn especially strange because it's about an orphan very much like Kaeya. He was taken in and raised by the third master, and sworn brother of her son.
Weird, but okay.
Fourth up: Dwarkanath

And here we go- back to brother. Not even adoptive or adopted brother... just brother. The "brother" doesn't say anything about her unfortunately to confirm.
This one is a bit interesting because the Eremites call each other brother and sister very loosely- they consider the entirety of their group a family and this is addressed by one of the NPCs directly. (CN versionof the same)
While Dwarkanath and Iraj aren't Eremites, it is a bit strange they're right there.
Conclusion:
I got nothing.
This literally makes no sense.
Blood related brothers are Sworn Brothers,
Brothers are also Sworn Brothers.
Sworn Brothers are Adoptive Brothers.
So I guess by the translation team's logic- Blood related brothers are adoptive??? They keep equating all these terms and dynamics to mean the same thing. They even flip flop the meaning of 养子 here and there too. It's hard to tell if they're trying to do it based on context or frankly just being lazy. This gets so difficult to search and track what is being called what and when/where. Some of it is contextual but a lot of it just doesn't make any sense. I'm so tired.
I honestly think the localization team is just as confused as we are at this point.
Next time I may go over all the different times adoptive/adopted/foster father are used. Did you know ELZER calls Crepus something like a Sworn Father to him? Fancy that.
Catch you next time;
Remember to ship and let ship- if you don't like it, don't read it.
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