Right, some information is encoded in the egg. You can't take human DNA and put it in a mice egg. And then you have the womb which itself directs growth in the first stages.
DNA is the machine code, but you need a compatible computer to run it.
There is some information in the cytoplasm, but how much? Human nuclear DNA encodes something like 8 billion bits of information; mitochondrial DNA a bit more (although there are many copies of mitochondrial DNA in a cell). The specific sequences of all the proteins and such in the cell is a consequence of DNA sequences; it's not a separate (or transmissible) information pool.
That human DNA produces a human when in a human cell doesn't mean the rest of the cell is carrying significant amounts of information, just that that's the environment in which the DNA has evolved to operate.
A piece of clay comes from a mountain and is pressed into a mould, then thrown into a river and melts, it lands at the end on a rock, squished. Why is it that shape?
To say, "because of the chemical composition of the mountain" is, at the very least, foolish.
Organic lifeforms are self-modifying clays that are pressed into environmental moulds. Genes play both a far more complex, and far simpler role, in this than the mid-20th C. eugenicist biological science supposed. A pseudoscience that still predominates in how people think about genes, and in many downstream research areas (eg., https://slatestarcodex.com/2019/05/07/5-httlpr-a-pointed-rev... )
The problem is none of that is information in the sense of something that can be acted on by natural selection. If it isn't copied from generation to generation, it's can't be molded over generations by differential survival of variants.
DNA is the machine code, but you need a compatible computer to run it.