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Unfortunately, without being able to see some signs of the exact cause, I can't really give much recommendation on the treatment. There are quite a number of factors to consider. Things such as overwatering, underwatering, insects or other pests, nutrient deficiencies or excesses, and more.

Taking a guess, I'd say that it is bacterial or fungal, but this is nowhere near an answer. This is just a guess because of the time of year. From here, to get an accurate answer, I'd recommend testing all of the parameters that you can. Testing soil pH, nutrient levels, moisture levels, and inspecting for insects or pests will be the first step. If you'd rather have it done for you, then you can take samples to your nearest extension service.

https://www.gardeningknowhow.com/garden-how-to/info/what-is-extension-service.htm

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/soil-ph-plants.htm

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-moisture-in-plants.htm

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-percolation-in-soil.htm

https://www.gardeningknowhow.com/special/urban/contaminated-soil-city-gardens.htm

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/test-soil-for-pests-and-diseases.htm

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-soil.htm

Yes, you can cut back the foliage. The fungicides typically don't help if the plant already has powdery mildew. Fungicides work better as a preventative than as a solution to fungal infections. The best thing to do is to make sure your peony is in full sun or at least mostly sun. Powdery mildew creeps up when a plant is too shaded. Also, be sure to pick up any fallen leaves so you can reduce the incidence next spring. You don't need to replace the mulch, but be sure you get all the fallen leaves.

Here is more:

https://www.gardeningknowhow.com/ornamental/flowers/peony/powdery-mildew-peonies.htm

Peonies generally don't like to be disturbed, and as old as those are, I would be hesitant to start now. They don't need to be divided unless you want to increase your stock of if they are not blooming well. If you have several, you may want to dig up only one and divide it, and see how it does. It may take three years for it to bloom. Here is more:

https://www.gardeningknowhow.com/ornamental/flowers/peony/dividing-peony-plants.htm

https://extension.psu.edu/the-beloved-peony