Gently placing a plant in a larger pot and covering it will not shock the plant. Did the rootball fall apart in the process? If potting up regularly causes a shock to the plant, i'd suggest a different hobby, LOL... i say that assuming this is not the case and likely some other cause behind it.
e.g. looks like that soil is devoid of drainage amendments... if coco-based should be 33% of volume and if something heavier like sphagnum peat moss-baed, you want 50% of volume. I'd recommend vermiculite over perlite, but it's mostly insignificant which you choose as long as it isn't big and chunky to the point it physically impedes roots.
could be genetics too.. growth rates vary by seed even when the plants are supremely healthy.
that drying pattern looks like you aren't using orthodox watering methods, either. Fully saturate and never partially water. if such simple things cause a problem or droopiness following an irrigations, then it is the fault of how the medium was constituted.
It's a myth that you shouldn't pot-up autoflowers. Just something that gets repeated but is not true. Potting up wil not shock a plant. However It definitely helps promote a healthy rootball development, and it avoids fucked up irrigation methods trying to mitigate the numerous real problems of having a tiny plant in a very large pot. Way more risk related to a tiny plant in a large pot than gently potting up. With enough moisture and roots, it will hold itself together through the process. Shouldn't be potting up before that point anyway.
"Transplant shock" isn't related to potting up. That term refers to cutting through roots of plants outside in the earth, which is incredibly stressful for the plant. I think this myth stems from a misunderstanding of vocabulary....