I've spent the last twenty odd years being militantly anti-alignment but I've mellowed and am now somewhat less evangelical about the position. Probably in part because 4E and 5E massively cut down the mechanical implications of Alignment which made it easier to run games without a very weird and specific cosmology baked into it.
Back in 2015 I did a compilation of all the mechanical effects in the 3 core rulebooks and posted it here.
Aside from a few scant mentions in spells and monster powers most of them turn up in the DMG in the descriptions of the Outer Planes (understandable) or in the Magic Item sections, mostly around artefacts and intelligent items.
Personally I quite liked Personality, Bond, Ideal and Flaw as a set of training wheels for new players to think about what their character cares about, but would be interested to know if new players actually did find them useful.
How do I think Alignment will appear in One D&D? - In short I don't think it'll be much of a new approach.
Based on:
1) 1D&D seems intent to be reasonably restrained with changes.
2) The 9 Alignment is a core part of the identity of D&D* and has entered pop culture parlance. Even if the role, rules and definition of the Alignments have changed substantially over the five decades.
3) Alignment hasn't been mentioned much in supplements unless they involve the Outer Planes. They're still in monster & NPC stat blocks but it seems more and more common to see "any alignment" listed as there is some effort to move away from biological essentialism.
4) From what I've seen the DMG is going to receive the most changes out of the core 3 books as Crawford et al are the least satisfied with it. I don't have a single source to quote for this however.
I am pretty sure the nine alignments will be kept but will have an even more diminished roll. Maybe some of the few spells, monster abilities and magic items get rewritten to entirely erase mechanical effects.
Alignment (or PBIF for that matter) hasn't been mentioned in the single PDF we've got. But this isn't exactly surprising since there isn't anything really to playtest.
(*Well more AD&D, as Looking at PDFs of older editions of Basic I didn't realise that Moldvay 1981, Metzer 1983 and Rules Cyclopedia 1991 all kept the original 1974 "Law vs Neutrality vs Chaos" and that Holmes 1977 appeared to have 5 alignments LG, CG, N, LE, CE but not NG, LG, CG, NE. Likewise I always thought that 4E's Lawful Good, Good, Neutral, Evil, Chaotic Evil worked well.)
What would I like to see Alignment will appear in One D&D?
Whilst I would have said "Gut it out of the system like a fish"..
... My ideal approach would to essentially be an optional rule and have Alignment in the PHB solely at the end in the Appendix alongside the Great Wheel's planes of existence.
Then have a similar entry in the DMG which includes discussion and optional rules of how to make Alignment more relevant in games but perhaps alongside other optional morality systems such as Honour and Corruption (probably a better name than Sanity).