Javascript Date plus one, plus two etc...

Try this:

var currentDate = new Date();
var player = GetPlayer();

//1DaysAhead
var oneDaysAhead = new Date(currentDate);
oneDaysAhead.setDate(currentDate.getDate() + 1);
var oneDaysAheadDateString = oneDaysAhead.getDate() + " " +
    oneDaysAhead.toLocaleString('default', { month: 'short' }) + " " +
    oneDaysAhead.getFullYear();
player.SetVar("oneDaysAhead", oneDaysAheadDateString);

//2DaysAhead
var twoDaysAhead = new Date(currentDate);
twoDaysAhead.setDate(currentDate.getDate() + 2);
var twoDaysAheadDateString = twoDaysAhead.getDate() + " " +
    twoDaysAhead.toLocaleString('default', { month: 'short' }) + " " +
    twoDaysAhead.getFullYear();
player.SetVar("twoDaysAhead", twoDaysAheadDateString);

// add your other offsets the same way…

The issue is that in JavaScript you cannot redeclare the same variable name (player) twice with let inside the same block. Redeclaring let player again causes the script to stop. Also, you don’t need to recalculate currentDate inside each block.