Is my nursery space set per season?

No, you set it once for the farm and it holds for every season: one less thing to redo each year.

To change it, click the figure in the Nursery space box next to the graph, type the new surface and confirm with the check mark.

Looking at a past season, the box shows your Peak nursery usage for the season instead: the fullest week you had, useful before you decide to build another table.

The steps are in Set your nursery space and containers.