What does engulfing the earth mean to you? The mass of the sun expanded to a body 1 au would not be very dense. My money says the earth would continue to orbit “inside the sun” for quite a while, but the orbit would degrade more quickly.
But yes, I argue get them out of the earths gravity well and let Newton handle the rest, no reason to propel them in any direction, eventually they’ll get to the sun.
If the sun became a red giant tomorrow, and Earth found itself inside the outer layers of solar atmosphere, then drag would start slowing it down. In less than 70,000 years, it would fall close enough to the center to be torn apart by tidal forces like one of Saturn’s moons (assuming it hasn’t already been vaporized).
If we’ve already waited 5 billion years to have our revenge, whats another 70k? The lowest amount of Delta V we can spend on this project is zero.
