AZD1222, the AstraZeneca covid vaccine, uses an adenoviral vector to deliver DNA to human cells that then produce the desired viral proteins to present to the immune system.
This is a bit much for me to read without the right background. I'll focus on your claim, though.
"Sending mRNA to human cells to produce viral proteins" describe how all of the other vaccines work. You're saying that this one uses DNA. I don't know if that's a typo or if that's an important difference. However from what I understand, the two other vaccines people are talking about don't change any of the genetic material in your cells. They just send other genetic material that makes use of the translation equipment in some of your cells. It sits next to your existing genetic material, and then (I'm guessing?) just goes away.
Yes, this one uses a DNA virus as a way to deposit a piece of DNA into the nucleus of a cell, so that it makes viral proteins the way cells usually do. The virus used is incapable of replication so it only has the cell entry features, not the viral propagation features.
Depositing a piece of DNA into the nucleus doesn't seem to me to be the same as changing the organism's DNA. If the cell divides, will the daughter cells each have their own copy of the DNA? It doesn't sound like it to me.
Apparently not. Wild-type adenoviruses seem to prevent cell division while they replicate their DNA on their own until they cause cell lysis to distribute the virions. Adenoviral vectors, on the other hand, leave the free DNA particle in the nucleus where it gets transcribed to RNA but it does not get replicated during mitosis.
