How do I change next year's number of draft picks that are shown on Picks pages?

Commissioners can adjust the number of draft picks shown and made available for trading in future seasons after this season's draft.

Here are the steps to take:

Go to League > Settings > Add a Supplemental Draft (this will bring back the draft settings)
Go to League > Settings > Configure Draft and set the number of rounds you want next year (this can always be changed later if needed); hit OK
Go to League > Settings > Edit Rosters and in the bottom Keeper Options section, select "These are complete rosters for this season" and click Save