Wa alaikum assalam
The term admits shades of meaning depending on context. The term 'al-nas' can also describe broadly the entire human race. Please kindly see just two examples below:
11:103 "…that is a day mankind (al-nas) are to be gathered…"
010:24 "…the plants of the earth mingle with it where mankind (al-nas) and cattle eat…"
As I have mentioned in my writings, the Prophet was tasked with a responsibility to convey the message of the Quran in Arabic to his people as a witness to the truth. His people had a responsibility en masse to pass the message to mankind (22:78) as witnesses to the truth. This would imply a discourse both in Arabic and an ability to convey its meaning to those who did not understand the language.
"...The messenger is a witness over you and you may be a witness on mankind (al-nas)..." (22:78)
Please also kindly note above how the responsibilities are clearly delineated. There would be no point of his people passing the message separately on to wider mankind as witnesses to the truth if the intention was to reveal the Quran to a specific people exclusively. In that case, the Prophet would have sufficed as witness.
I hope that helps, God willing
Regards,
Joseph