I bought some basil with roots to plant inside. Brought it home, divided them and planted them in some fresh potting soil, clipped them back, then watered. 3 days later it looks like this. Yikes!
Yuk! I wouldn't have divided them, only put them asis in a large pot.
Also, what was the reason for cutting them back? And does that pot have a drainage hole? They look as if they may be too wet and possibly have got too cold. Is it chilly near that window?
They've had multiple nasty shocks. Disturbed roots, decapitation and a change of climate. All you can do is wait, hope and not water for a good while.
I'm betting that when you divided them up, you were quite rough with them - yanked them out, breaking the baby roots, instead of treating them very tenderly and easing them out gently. That's an unintentional mistake made by many beginners. They're babies, remember, and those roots are fragile.
I'm also willing to bet they were handled quite roughly when transplanted, too. Stuck in the dirt without having a little hole prepared for them with a stick or pencil (a dibble). More root damage as a result.
They probably weren't gently tamped in with the finger-tips, just enough to help them stand up straight. Possibly they were just flooded with water in the hope that it would eliminate air-holes/spaces in the soil to stop the seedlings from collapsing.
Then they've been over-watered to the max, and the water gathered in that saucer - result - no drainage.
All is not lost. I see one survivor in that little field of death. Nurture it. Leave it where it is and try not to kill it with kindness.