How do I see the next 12 months instead of January–December?

Switch the year view to Rolling. Open the calendar menu and choose Year Range, or open it from the bottom of the year picker. Under Mode, select Rolling, then use Start month to begin from This month, Previous month, 2 months ago, or 3 months ago.

The view moves forward by itself each month, so the months ahead stay in view. If you want the year to always start from a specific month, such as April or September, use Fiscal mode instead. Year Range is set per calendar, and only the calendar owner can change it.