It's really unclear what's next for the HGP. While HGP and many other sequencing projects have been invaluable to academic research, and it's truly useful for a number of diseases, the main result of the HGP, in my mind, is that it made clear to everybody how much harder the genotype->phenotype problem was than what the geneticists who set up the HGP anticipated.
Medically speaking, there isn't enough evidence to support the cost of doing WGS for individuals in most circumstances, or even storing large amounts of WGSs to do large-scale population-level analysis.
There are a number of successors to the human genome projects, which to various degrees of success have mapped the epigenetic landscape around protein coding genes.
However, your point is pretty spot on: what's the medical value? Having really high resolution epigetic maps doesn't translate into better clinal results, and it's not even clear that the results of these studies are looking at anything but statistically confirmed artifacts!
The HGP definitely had value, but almost all of the "massive" data collection projects in biology have since been basically useless, except for the consortia who got paid to do this. Leave medicine, no one I know of even uses any of these datasets even for research if at all they're made available in a browsable format.
Only exceptions I've seen are the cancer cell line encyclopaedia from broad and the c. Elegans rnai projects.
The HGP likely sped up the COVID vaccine - by making DNA sequencers and printers cheap. Viral genomes are typically obtained by taking a swab from a human, mapping the reads to the human genome, so only viral sequences are left.
A thousand different technologies were required to make the COVID vaccine. Having the HGP helped, that's for sure. My main complaint is that the HGP leaders basically sold the public and government on a list of accomplishments that never materialized, and yet the underlying data has been invaluable in a wide range of different health problems that they didn't think it would be useful for.
DNA Printers, or a technique known as "solid phase synthesis" is a different technology that was used by the HGP, but not developed or advanced by them.
I remember using these 20 years ago to make RNA (they can make RNA as well as DNA, if you add the right reagents, which IIRC were obscenely expensive). They'd run with various pumps and relays clicking. I got 40 OD of a single RNA duplex, and proceeded to... wash it down the drain, since I was an idiot in the lab.
By "making... cheap" the mechanism I meant was it drastically increased the market size for genomics, and thus ushered in economies of scale in these technologies.
Medically speaking, there isn't enough evidence to support the cost of doing WGS for individuals in most circumstances, or even storing large amounts of WGSs to do large-scale population-level analysis.