Are these really one-time purchases?

Yes. Every paid app is a single purchase between $1.99 and $4.99 with a free 7-day trial. There are no subscriptions, no accounts, and no in-app purchases.

Which watches are supported?

Most Connect IQ-capable Garmin watches from the Fenix 6 and Forerunner 945 era onward, including Forerunner 165 through 970, Venu 2 through X1, Instinct 3, and current Edge units for the cycling-relevant fields. Check the store page for the exact model.