Money for HPSP does not come out of the same personnel funds as career Civil Service, those positions are considering Training and Education. You're safe on that score. Those on multiyear positions in training (medical residents) have their funding guaranteed as well, it does not come out of the same personnel funds. There are specific legislative safeties in place to protect those from curtailment (withdrawal of positions or early termination of personnel).
Of the 8 VA positions I interviewed for, 6 of them pulled the plug with emails saying the position has been "cancelled and not be filled at this time." One position went to someone else (specialty position to someone with more experience), and the other had to email me back and forth for the past 2.5 months saying that the position needed to be approved on 3 separate occasions, but finally sent a tentative offer (which honestly, could be pulled anytime as well).
Things have changed since last time I tried to apply (2021) but was told the slots were already filled. At least on SDN, you may be the only active user who is currently applying. Presuming you hit the check marks and the availability has no merit on the current conditions, I'd say you'd here back 3-4 weeks at the latest (if its the same person I communicated with a few years ago).
