Dear all,
...since I had never been on a plane myself, it seemed the most natural thing in the world to me that the prospect of her first flight should fill her with excitement.

In the sentence above, what is the meaning or function of should?

If it's would, which is more familiar to me, is the meaning different?

I understand should is more frequently used in British English than in North American English. Since I learned American English, "should" seems to be one of the least familiar words among basic words.

Thank you!

OP