The panspermia idea makes no sense

So ya know how in the book they mention how 40 Erdani and Sol's life was proably seeded by Tau ceti? It's a cool idea for the plot but dosn't make much sense especially from a writer as grounded as Andy Wier. Not because of stuff like how the life got from tau to the other systems. But when... It's stated that the hypothetical panspermia happened billions of years ago. This dosn't make sense for two reasons, Mitocondria evolved on earth after life first showed up so it makes no sense astrophage has it. But second and more importantly, stars move. Because of the movement of stars even if tau could seed Erid and Earth it would only been able to do it during a few hundred thousand years window max where both are near enough to it. But since it's cannonicly billions of years ago when it happened this shouldn't work, tau ceti has not been near us for that long, same for Erid. So it dosn't make sense that if we were close enough to be seeded back then that we'd still be that close, Sol, Tau, and 40 Erdani aren't close together enough to be gravitationally bound to eachother so it makes no sense that we'd still be close to the same stars billions of years of stellar drift later.

Dosn't matter much though it's a cool plot.

tldr: If tau seeded Earth and Erid billion sof years ago stellar drift should have seperated us from them by now.