There was no forward business, no futures, nothing.

The forward curve is simply the price relationship between different contracts months at a point in time. The prices could represent futures contracts or even physical forward contracts calling for delivery of a commodity.

When prices of subsequent futures contracts are charted a so-called forward curve is created.

I tend to use 2nd-3rd to avoid delivery squeezes distorting the long-term charts. But, evidently, better to look at particular months where the hedging (and OI) accumulates. But for a long continuation chart, a 2nd-3rd, typically shows the trend.

function of all futures prices at a specific moment in time¹⁾

price curve exists of today's spot, 3M, 6M and 12M prices plus all other futures dates²⁾

the curve reflects what the market thinks today of a commodity price in the future³⁾