I want to explore Hokkaido in September and have successfully booked flights and the first two nights in Sapporo.

However, I am having trouble finding hotels in Toya-Ko Onsen , Noboribetsu and around Shikoku-Ko. Also in the north east of the island. Most of the larger places are fully booked six weeks out and many towns list nothing at all on hotels.com or booking.com.

Am I missing something or is Hokkaido, outside Sapporo, full in September? Some reviews seem to suggest that hotels have not fully reopened post covid but I thought that problem would be over by now.

I really want to visit Hokkaido but am now thinking of changing plans completely!

That ... I was trying to book a traditional Ryokan in Akita and was told that they are not taking many guests due to the lack of staff ... the typical inns have a lot of elderly staff that might have retired during COVID and are not coming back.
I would still visit Sapporo, however, if you have not been there before. it is a great place to explore and to enjoy the food as well!

Have you tried booking on some of the more Japanese "local" web sites -- here's a short list but there are so many more: Japanese Hotel Reservation Sites

We travel to Yamaguchi prefecture often and the major international sites rarely have anything -- but the local sites often do.... It is true that many places have closed or reduced staff due to COVID -- but they are coming back now.... My wfie uses Jalan to book almost exclusively....

Seconding the recommendation to use a Japanese booking site. I use Jalan.net, I find their layout more intuitive than Rakuten which is the other big website.

Once you have found a ryokan you like, compare the staying plan and the price versus the ryokan's official website and the western hotel search sites as sometimes one is cheaper than the others or has a better selection of rooms and dining plans.
For example, I am very familiar with western affiliate cashback sites (~5-7% depending on site and valuation) but do not travel enough to want to deal with Jalan points, so if everything is the same then I will book via booking.com.

Then book.

Friendly reminder to make sure you are using the Japanese version of these websites. Use Google Translate if you need to - but the selection can be quite different from the English website.

And with online translation, you can ensure you are getting the same room etc.