Traveling from Tokyo to Amanohashidate

When traveling from Tokyo to Amanohashidate, is it realistic to transfer within 10 minutes in Kyoto? Wondering if to buy a ticket as one trip or 2 tickets separately to allow more time for the transfer.
First time in Japan traveler. Thank you!

You should buy the tickets for the entire trip together.
Being familiar with Kyoto Station and Japanese train system, I could make the transfer within 3 minutes. On the other extreme, if you tend to have problems finding your way in your own country or have lots of luggage or are not the fastest walker, it may not be enough time. For a majority of travelers it should be enough.

When traveling from Tokyo to Amanohashidate, is it realistic to transfer within 10 minutes in Kyoto?

Yes. Google maps tells that it will take 3 min to transfer from Shinkansen to the local limited express Hashidate.

Wondering if to buy a ticket as one trip or 2 tickets separately to allow more time for the transfer.

You may better to buy a ticket from Tokyo to Amanohashidate. If you are staying not Tokyo station area such as Ikebukuro, you don’t need to pay Ikebukuro to Tokyo section which is included in Tokyo to Amanohashidate ticket.

By the way have you considered JR west passes which might fit your itinerary?

https://www.westjr.co.jp/global/en/ticket/

If you want to use one of these passes, you will need to pick-up your pass at Kyoto station (you can’t at Tokyo station). In this case, 10 min is not sufficient. But Nozomi Shinkansen is very frequent (every 5-10 min) so you can adjust your departure time at Tokyo.

3 min walking time seems a bit tight. But there are literally Shinkansen to Kyoto every few minutes. So just get a Shinkansen 10-15 min earlier and you don’t need to rush. And May even have time to buy a drink or some lunch at Kyoto station.

You should definitely buy 1 ticket not 2 as it is cheaper.

Am I missing something? My understanding is that you can board any JR train, along the route, using one through basic fare ticket all the way from Tokyo Station to Amanohashidate Station. And you need separate express fare tickets per express train anyway.