Google Translate via Chrome says
[Important] [Reservation acceptance period] Currently, Azumi Setoda << March 2, 2021 --May 31, 2021 >>
https://go-setoda.reservation.jp/ja/...da/searchInput

Most Japanese ryokans allow bookings 3 to 6 months out.

Clicking through the availability calendar only shows bookings with breakfast, no dinner.
https://go-setoda.reservation.jp/ja?...ld4=0&child5=0

Base rate for the less expensive yubune side and bottom tier room with shower, Thurs night breakfast only, 2 guests is 22,000 JPY
Base rate for the Azumi Setoda side and bottom tier with a bath tub, Thurs night breakfast only, 2 guests is 78,100 JPY.

Location is in a town https://g.page/yubune?share so you might be able to find dinner but honestly, that price should include it or offer it as higher price package. If you think you'd have more flexibility of dining times and cuisines by not booking dinner with a nice ryokan, this isn't a big city. Clicking around on Google Maps shows a neighborhood sushi shop, izakaya, ramen shop and a couple other options.

Website also does not mention if the cypress bath has onsen water which I'd also expect for that starting price range without dinner and another web page about the main bath house. The main bath is done in the city sento style https://azumi.co/yubune/#accommodation and 900 yen for non-guests during 10:00 to 20:00. Both the room rates allow for stays at 16:00 to noon which is a little later check out than many ryokan. Keep in mind breakfast might be offered at a specific earlier times so sleeping in may forgo breakfast.

I spotted Mari in Setouchi a couple years ago https://setouchifinder.com/en/detail/6778 which is known for local foods and a soy sauce kaiseki since it is in a soy sauce manufacturing district.
They opened a more contemporary seaside inn in 2019 https://uminoshijima.com/#section01 (sound warning)