natural shading by plants

So I think the idea is very nice. Besides, the shade under a tree is much more pleasant. It is important that the shrubs have a rather umbrella-shaped crown so that they provide shade over an area. You can train almost any shrub that way (or buy it accordingly). What matters is that the plant is branched out lower down. Google "umbrella-shaped shrubs" or check the site schirmförmig(punkt)ch, there you will find information and pictures. Non-native species attract fewer insects.

Plane trees with espalier are fantastic. They do not grow very fast, in the first summer shade-giving trees are costly.

I would think about the dirt from leaves, flowers, and bird droppings and all the wooden grooves where it gets stuck.

I don't, occasionally sweep through and that's fine. You gain a lot of quality of life with little additional effort.
Calling fallen leaves and flowers "dirt" sounds pretty disconnected from nature.

that the trees have a rather umbrella-shaped crown so that they really provide shade over an area.

There are also trumpet-shaped ones. Their growth form looks like a chanterelle, like in the picture.
Yes... it looks awesome. But I also think about dirt: such a tree drops a lot every day, either through animals or wind. Don’t take one with fruits, so no serviceberry, as it attracts birds and drops mushy fruits.

As much as I love being in nature.. I don’t want it like that on the terrace either. The factor of dirt would bother me too much here as well.

Is such a natural shading practical? The distance between the crabapple trees is exactly 5m

Do you have enough space around your wooden deck for the plants? If I add 3m on each side because the trees also have their crown beyond that, you would need a base area of 11x11m.

Otherwise espalier, with whatever plants (that make a mess on the terrace).

Looks very stylish but is it practical? If you sit so close directly under the trees, you have all kinds of creatures around you. Spiders, bees, caterpillars, ants... that might be a nice change for a picnic but every morning at breakfast?