At what point are the effects of the Genocide route irreversible

Your source is correct. Flowey remembers that you killed that character, but only mentions it once, and it doesn't affect your ability to reach the True Pacifist ending in another playthrough. This is true of any character in the game that you can kill--if you revert your save to a point before you kill them, for the purposes of reaching the True Pacifist ending, it will be as though you never did so.

The only thing which will permanently alter the state of your game is

completing the genocide ending

which can still be reversed by deleting your save file or uninstalling/reinstalling the game.

Go to Users\yourusername\AppData\Local\ There should be a folder called "UNDERTALE". If you want to remove absolutely everything, delete that folder.

If you're playing on the Steam version, make sure you disable Steam Cloud for the game as well.