although very rare and difficult to get it from a spit on a meal i would make vaccine anyway
for example i have problems with my gums and when i eat an apple i leave blood on it, same thing when i wash my teeth i lose a lot of blood, so you find blood in my saliva and virus too, i guess even a kiss from me can be contagious, fortunately in my country vaccine is mandatory at birth from the '80 so i cannot spread hbv anywhere
the chance is low and contagios rare but the virus is present in the saliva so you must get the vaccine to be 100% sure.
the most contagious are people in the immune tollerant state who have from millions to billions of hbv in the blood.
hbv is at least 100% times more contagious than hiv and the virus can live 7 days on objects and surfaces
In the scenario you describe no. But hep b can be passed through saliva although the main methods are blood and sexual bodlily fluids
You can't get Hepatitis B from saliva. Hepatitis B is blood borned virus and STD.