Despite coming across like I was trying to correct you, I only meant to give my personal understanding of “handful”
I don’t know where I got my idea of handful, but it probably came from how high I can count using the fingers on one hand. So far that understanding seems to work for me when other people say it as long as I do what you said and treat it as an approximation.
On the “several” topic, I used to think it meant “about seven” because of the shared “sev” prefix, but it didn’t take long to realize several has a much bigger range than that.