Teaser 2958: Sudoku crossword

From The Sunday Times, 2nd June 2019 [link]

George and Martha are doing a mathematical crossword. There is a 3×3 grid with the numbers 1 to 9 inclusive appearing once each. The clues are as follows:

top line: a prime number
middle line: a prime number
bottom line: a prime number

left column: a perfect square
middle column: a perfect square
right column: a prime number

Although you do not need to know this, one of the diagonal three-digit numbers is also prime.

What is the sum of the three “across” numbers?