Is that correct that a complete DNA sequencing (the whole genome) need
only to be done once (per person)?
Likely, yes. But I think you vastly overestimate how often this is done. If someone gets their DNA "sequenced" at 23andMe, for example, they are not getting their whole genome sequenced. They are getting individual bits believed to be possibly clinically relevant sequenced. It's a different technology than you would use to get the whole genome. A whole mammalian genome is really big, therefore kind of expensive to sequence, and is mostly non-coding DNA of questionable relevance. Therefore you can just genotype the exact bases of interest, or maybe do exome capture, which gets you full sequence for the 1% or so of the genome that is currently annotated to be coding. Obviously either of those approaches would no be all-inclusive, so one might wish to redo them at a later date with new targeted regions of interest.
Even if you did get a whole genome done with current technology, right now it has limitations, namely read length, that make it hard to work out certain details. I could easily see someone needing to redo a genome using a longer read technology, when that technology arrives.
Also, we aren't really discovering that many new genes. Certainly not protein-coding ones. What is more likely is that we discover that variants in this or that gene might be clinically relevant to some health parameter.