The word “design” has many uses in English. There is a loose usage in which we speak of any apparent pattern as a “design.” One might speak of a design of frost crystals on a window pane, for example, or of a “design” of wavy lines in sand on a beach. However, in the context of origins discussion, I restrict the use of “design”, and it always implies planning, foresight, intention. That doesn’t require any specific religious belief, e.g., Christianity or Judaism or Hinduism or the like. The idea is of some sort of mind or intellect behind nature, which could be conceived of in various ways, theological or philosophical.
So no, I would not call a product of a process of trial and error a design. I would distinguish between real design and apparent design. What you get in Darwinian evolution, through trial and error processes, is apparent design. Natural selection, in conjunction with other things, is a “designer substitute” – it produces results which look as if they were designed.
Of course, in loose usage, one could speak of Darwinian processes as “designing” better beaks or longer necks or better camouflage, etc., and often enough in everyday conversation, I would let such usage go without making objections, because one doesn’t have to make every casual conversation into a rigorous debate over chance, selection, design, etc. But in settings like this, I think it’s clearer if I stick to one consistent meaning of the word “design”. I can’t compel anyone here to adopt my usage, but it’s best if I announce my usage, so that unnecessary quarrels over words can be avoided and the focus can remain on substance. There is a substantial difference between “design” as someone like Paley meant it and “design” as many fans of Darwin mean it, and for me, the best way of keeping that substantial difference in mind is not to use “design” for what Darwin was talking about, but to restrict “design” to the planning of some sort of mind.
As to how the design is implemented in the natural world, whether by miracles/interventions or by some sort of unfolding natural process, that is a different question. I’m here explaining what I mean by the term “design”, not making any claim about how design is implemented.
Under my definition of “design,” I think it is safe to say that the “mainstream” view of evolutionary biologists is that the process of evolution is not in any sense “designed”, even though it may often produce results which are as effective as the results of design. Regarding the origin of life, which is outside of evolutionary theory proper, I think it is safe to say that most of those involved in origins of life research are looking for ways in which life could have come about without design, i.e., without foresight or planning.
I trust that this clarifies my terminology. It does not settle whether or not anything was designed, but I took it that the purpose of your question was to find out what I mean by the word, and how I plan to use the word in these discussions.