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It is usually advised to remove plant residue in the fall, because of overwintering disease and insects, and replace it with mulch, such as straw, shredded leaves, grass clippings, or wood chips. They will begin decomposing during the winter and can be tilled under in the spring. You also can plant a cover crop such as winter rye or alfalfa to till under in spring. Also, leaving it may produce volunteers, which if the plant was a hybrid, won't come true from seed.

If you feel comfortable that no disease organisms or insect larva are present, you can lightly cultivate the plants to break them into smaller pieces. Avoid tilling which will disturb the good soil fungi.

https://www.gardeningknowhow.com/edible/vegetables/vgen/winter-vegetable-garden-tasks.htm

https://www.johnson.k-state.edu/lawn-garden/agent-articles/vegetables/vegetable-garden-cleanup.html

It looks like sunscald. Make sure the beans are getting about 1 inch of water a week, and if the sun is very intense, you can erect a shade screen during the hottest part of the day. These articles should help:

https://www.gardeningknowhow.com/edible/vegetables/beans/growing-pole-beans.htm

https://www.gardeningknowhow.com/garden-how-to/info/shade-cover-tips.htm

Here are more issues to watch for:

https://edis.ifas.ufl.edu/publication/PG041