Now we’re into cultural issues. In the UK hugs are reserved for close family members and generally given in private. Hugging acquaintances and strangers is not the cultural norm over here.
Yes, hugging (in my culture) means:
“I’m happy to see you.”
“Good-bye”.
“Great game.”
“Great job.”
“Thanks for inviting me over.”
“Peace of Christ to you” at Mass
Hugging strangers - meaning someone passing on the street - is out.
Being introduced to a friend’s friend may mean giving the friend’s friend a hug when you say “good-bye”.
A hug can mean “welcome to our circle of friends”.
My son is living in a very primitive setting in the jungle in South America made up of people from various countries - mostly from the US. He is the “official greeter /hugger” when someone comes into their valley. “Welcome. You are among friends” is what the hug means.
If you were in my home, I would “read” you to see if you might welcome a hug. If I notice I thought you might not want a hug I would do two things 1) not hug you or 2) ask if I can give you a hug.
At the Sign of Peace in Mass, I would shake your hand. If someone hugged me, I would hug them back.
(I would also be aware of any “gut feeling” that told me to be caution and not to hug someone even in Mass or any place. Those feelings are not cultural. They are instinct and sometimes our guardian angel protecting us. )