So I stopped by a local Barnes & Noble bookstore and glanced through the core books there. Here are the printings I found there:The last errata was December 2021: D&D 5e Errata
There might be another printing, but it's probably identical to the December 2021 edition.
1E phb was reprinted 1990 after 2E launched.I can confirm the 2014 Player's Handbook has a 17th printing, and it looks like there's an 18th printing also, with the new styling for the lower caption on the cover, as seen on 5e books from at least as far back as 2023 like Quests from the Infinite Staircase and The Deck of Many Things™. I spotted the copy below on Facebook Marketplace (not my photo).
Interesting that its sales remain brisk enough to keep it in print even after spending big bucks to replace it with a new edition. Did TSR keep the 1e PHB in print at all after releasing 2e's rulebooks? Did WotC keep printing the core 3e books after v.3.5 hit?
I should note that no copies of the DMG or Monster Manual on eBay that I could see have this change to their cover, so those two are either actually out of print or just selling slow enough that the reprint timing hasn't hit yet. However, I have also spotted Tyranny of Dragons with the new caption styling, so the change is definitely "making the rounds."
Wizards themselves mentioned in February or March that work was underway to reprint the 2024 PHB (as errata was being incorporated). I would assume that the 2nd printing is now out on the street. That said, I don't have direct evidence for that.Out of curiosity what printing is the 2024 PHB up to now?

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.