True.
The whole idea of an Intelligent Designer is a modern preconception,
Agreed. The growing body of scientific knowledge forced a rethinking of preconceptions by which Genesis had previously been interpreted.
piously meant, I’m sure, but entirely absent from a plain reading of Genesis.
I would disagree because inherent in the account is something every creative person understands and that is that you do not begin with the next phase of a project until design criteria for the present phase have been met.
In the Genesis account, God did not begin the next phase of creation until after he recognized the phase he was working on was complete and to his satisfaction... "And God saw that it was good". He knew what the desired objective was but needed some time to get there and only after recognizing that "it was good" did he begin the next phase.
The formula, “Let the earth bring forth” is repeated wrt the animals, but in that case it is added, “And God made the beast of the earth ...” where this is not said of the grass and other plants. Isn’t this an indication of the lesser status of plants?
Yes. I would agree.
Doesn’t this distinction fall afoul of our modern conception of the unity of DNA based life forms?
I don't see how it does but I don't claim anything beyond a layman's understanding of DNA.
Basically, plant life is a lesser (in complexity) life form and would have evolved first.
Sorry plant life is not lesser in DNA complexity. Generally, the more complex the DNA the sooner it goes extinct due to having very specific environmental and nutritional needs. Do an internet search for the DNA of the plant ‘Paris Japonis’ replacing the ‘marbled lungfish’ for the largest genomic footprint.