The term '弟弟' only refers to 'younger brothers' (include half brothers or adopted brothers). It doesn't include 'younger male cousin' which has its own specific terms '表弟'(younger male cousins from 1. your mother's brother or sister [姨表]; 2. your father's sister [姑表]) and '堂弟'(younger male cousin from your father's brother)
- both (姨)表弟 and (姑)表弟 are simply called 表弟.
*The same is applicable to '哥哥'. We do not address '表哥' or '堂兄' as '哥哥'.
The reason 杨昭 referring 杨锦天 as '弟弟' is clear from the excerpts
领养: to adopt (a child); to foster (a child)
杨锦天 was adopted by 杨昭's parents. They raised him as their own son.
Even if 杨昭's parents were not blood related with 杨锦天, he would still be called 弟弟 by 杨锦天
It is the adopting parent who decides whether to retain the relative title or not.
It hits the mark. Apparently, 杨昭's father did not treat 杨锦天 as his nephew (sister's son). He adopted him to be his 養子 (adopted son)
Your adopted brother, blood related or not, is closer to you than your cousins do.
Side note from comments:
杨锦天 should had a different family name before he was adopted by his uncle from his mother's side. It was natural for him to adopt the 杨 family name from his uncle, who had became his adopted father.