Woodpeckers and in particular this genus and its close relatives are large (this species was 60cm long), noisy, relatively easy to spot birds. They even frequent feeders. Plus they are cavity nesters which are easier to spot.
To have remained alive for the 80 plus years since a credible documented sighting they would need to have been above the minimum viable population for species survival which is likely around 500 individuals.
Not one of these expeditions or observers has managed to capture a recording or photo despite their claims of observing them. No general biodiversity evaluation or researcher studying some other taxa in the range has stumbled across one. No amateur with a camera or Facebook post of ‘what is the bird here I just saw’ has taken place.
They lived in well studied, well populated areas. While I would love for there to be a different answer, the odds overwhelmingly favour the species being gone.