Osaka-Kyoto-Hokkaido

Hello, would really need your advice on the following:

We'll be flying into Kansai International Airport, and then travelling around Osaka & Kyoto for about 4 days. After that, we will fly to Sapporo, and intending to travel around Hokkaido - Sapporo/Asahikawa/Furano/Biei/Otaru.

Will the JR pass be recommended to cover all of these travel around Osaka, Kyoto and within Hokkaido? Is the JR pass eligible for use on the Hokkaido rail up to Asahikawa for example? Or do I have to purchase a separate Hokkaido rail pass to travel within Hokkaido?

Thank you so much, really appreciate your help!