The GARDENA gardening expert
In case of ash, a waste product from burning in fireplaces in which only wood and briquettes have been burned, one would think that the resulting ash must also be a natural product. This train of thought is initially correct, but there is a catch, and this has to do with the fact that a waste concentrate has been generated as ash. For example, the ash contains all the heavy metals which a tree has adsorbed during the course of its life, which were contained in the burned pieces and which are now left in the ash. This means that the ash contains a concentration of all the heavy metals from the burned wood. In principle, this also applies for coal ash.
Both ashes are initially of interest as potash fertilisers, which plants require for cell maturity, resulting in more frost-resistant plants and tastier fruit. However, this advantage does not outweigh the disadvantage of heavy metal concentrations, which is why I advise you above all not to add wood and coal ash to the compost, and not to scatter it in kitchen gardens.
In minor quantities or if very sparsely scattered, however, you can indeed distribute it in purely ornamental gardens. But only so that no notable accumulations of heavy metals result in the soil. For who knows what the ground may be used for in future?
As far as your climbing hydrangea is concerned: in my experience, these plants are highly reluctant to flower if they are planted in too shady a spot. Climbing hydrangeas are stated as being for shady locations, and will indeed only do well in more shady positions, but actually flower better in half-shade and alternating shade than in deepest shadow. Climbing hydrangeas require a soil which is rich in nutrients, fresh, damp, loosened and permeable. They do not like lime or dense topsoil (for example, if their roots are used as a path to walk on). Here, too, your actual situation is to be compared and adapted to the requirements of the climbing hydrangea.