https://www.saltspringseeds.com/collections/non-staking-pea-seeds-pisum-sativum
These are considered non-staking peas. Although if grown in a solitary row, they do like a net. When growned in a block, they self support. Most traditional drying peas are like this as they would be harvested by scythe and thrashed. Sticks would risk damaging the scythe.
Soup peas is another common term here. Some container or dwarf varieties that sell for a lot here, look suspiciously like field peas. Maybe it's part of being raised in canada, we spent a lot of schooling watching documentaries of what the other parts of the country produced, so the arial footage of vast fields of peas and canola stuck in my mind.
Another issue, most of the medieval period in Christian europe didn't document mundane things like farming until about 1500, so there was a lot of interchangeable language between peas, chick peas, pulces, beans, lentils, favas, etc. It was pasent food and usually got lumped in legume (or a variation on that spelling). For more info, the scientific studies in Arab spain circa 1100 to 1450 has some great info, but very little translated into english when last I looked.
Fun fact, peas was both singular and plural for most of English history. It's not until the latter part of the 20th century that we get the word pea coming into common use. A bit like sheep and the new word, sheeps.