Ahhoi. Like the topic starter, I am in exactly the same "category" with regard to Permies, i.e. a long-term observer-learner but a first-time participant in the topic. I have experience with land improvement works, including excess moisture and drainage systems. If you look at the top picture, 1) it is clearly visible in the left part that the soil has started to collapse into the ditch, therefore this part cannot be soil with a majority of clay. Considering that the soil in the entire excavation visible in the picture has the same texture and color and the color does not vary, it can be concluded that the entire upper layer is soil with a similar and rather low clay content; 2) the vegetation in the adjacent area is bright green, which indicates a sufficiently rich soil; 3) it is evident from the side wall of the excavation that there are no differences in the soil layers; 4) there are also no different colors and possible layers noticeable in the soil lifted from the excavation; 5) in the upper left part of the picture, where there is an unmowed area, a taller growing mass is also noticeable. These five characteristics lead to the conclusion that in the trench visible in the upper image, the upper part of the soil, i.e. the part of the soil above the water line, is rather a rather valuable soil and the water is probably standing on the clay that came up exactly from the bottom of the trench. According to the lower image, one could assume that the water has actually decreased by about half or even more, at the bottom of the image, colorful stripes can be seen along the edges of the trench, they can only be caused by the water level or, more precisely, by a change in the level. In essence, this does not change the matter very much. In summary, we can say that 1) the clay in the lower layers is possible that it is not too heavy clay, because otherwise the water would not have decreased at all, or 2) the clay in the lower layer is strong but the water seeped into the lateral layers. I suggest that the following options could be considered: A) dig a deeper hole, or so-called control hole, in a couple of places (then it will be more certain whether the soil layers are the same or different in several places), to make sure what the soil layers are deeper. Speed is very important with this option, because it is likely that when digging, it can immediately overflow. It could help here if there is another hole next to the inspection hole, which is deeper than the inspection hole, and water that would otherwise overflow into the inspection hole can be directed there. This is easier said than done, of course. However, if an excavator is available, it is possible to deliver more efficiently. Or pump the water out. The idea of this option is to understand whether the clay layer on which the water remains is thin or thick, and whether it is expensive to make a deeper trench than this. Option B) do not make the trenches deeper. Fill the existing trenches with the filling necessary for the formation of good soil, which has been well described in previous posts, and use the existing and additional similar trenches as they currently function - this water is the wealth to use in raised beds. At the same time, build valves to the drainage ditch running perpendicularly down, which can be easily removed, like sluices or mini-dams, in case there seems to be too much water, then you let some of the water drain through the drainage ditch. Over time, i.e. after 1-2-3 years, as the organic matter added to the bottom of the ditch decomposes, more water will be absorbed and the need to divert excess water may decrease. This option assumes that the ditches have a sufficient but minimal slope towards the drainage ditch so that when you open your mini-dam, the excess water can also seep or flow away. Option C) combine option B with new lateral trenches running from top to bottom. You also fill these with organic material. When viewed from above, it looks like an S or multiple S depending on how many long trenches you plan to make, when you mentioned "series of swales". The idea of this option is that the water meanders through your desired areas and then the excess exits through a drainage ditch. The assumption of this option is that each ditch is sloped in the opposite direction so that the S can work.
