Well, it is fair to say that each PbtA game has a certain COLOR to it. They obviously each occupy a genre, and then within that genre they MAY invoke some specific rules that are either related to the overall genre, or provide this color. Of course some/all of it might also be provided by things like creatures, gear, etc. Surely the available moves and playbooks will form a significant part.
However, it SEEMS TO ME, that at least some of them are pretty darn general overall. That includes the 3 most commonly used games, Apocalypse World (which does post-apocalyptic Mad Max style play pretty well), Dungeon World (D&D adjacent Fantasy), and Uncharted Worlds (general Space Opera ala Foundation/Traveller/other 'harder' far future milieu).
So, I'm thinking about LotR here, for the sake of argument. D&D doesn't do this super well, despite drawing a lot of superficial details from Middle Earth lore, like many races of elves. LotR is true high fantasy. Despite addressing a scenario in which the characters traverse the land, journeying from one hazard on to another, it is NOT a very 'gritty' story. Instead it deals with personal growth, standing up against evil, personal courage, temptation, and with minor themes of redemption and obligation. Mundane things like equipment, food, finding a path through the wilderness, surviving said wilderness, etc. are all very minor peripheral parts, at best. Simply incidental plot devices. Likewise the author never really describes a living material world including all the details of people's lives and seeming LIVED IN to any great degree.
Yes, The Shire, and a bit of Bree, is brought to life, but that is about it, and mostly to contrast with the actual locations where the action happens. We learn nothing about how Bree supports itself (we can guess, there are enough details) but we have literally NO IDEA how Rivendell works, what do they eat? How do they obtain it? Where do all the materials come from for all their stuff? Is it all just elf ring magic? Likewise Lothlorien is not really depicted as any sort of realistic location you could interact with. Even Minas Tirith and Rohan (I forget the name of the town) don't really have any practical details (again, we could at least imagine some are unstated).
And this has always been the biggest problem with classic attempts to make an LotR-based Middle Earth RPG, from the days of MERP all the way down to today. Third Age Middle Earth isn't really a living world, its a stage on which to tell a certain tale, and any attempt to create an RPG which engages with ordinary everyday concerns, in any way, except as occasional plot devices, is doomed to conflict heavily with the atmosphere of LotR. I mean, MERP isn't a bad fantasy RPG, and it reproduces the MATERIAL of LotR adequately to a degree (IE you can make wizards and elves, and they do magical and martial things that sound like things that would be possible in Middle Earth) but it mostly fails on the 'color' front, the atmosphere is all wrong. This is because it fundamentally uses a play process that is pretty much lifted from RM, and ultimately from D&D (there are some differences, but it is still substantively a cousin of D&D).
Now, Dungeon World will, by default, hit some of the same issues. ME RP definitely is NOT about checking off boxes of food rations, or wandering around the countryside poking into every odd grey zone on the map. You COULD kinda make it work by focusing on fronts and whatnot that are existential threats, and playing up personal responsibility, obligation, and the 'step up and take it on' ethos of Frodo Baggins. Bonds, alignment, etc. would actually help with that. You would probably want to do away with most of the equipment rules, maybe use a model for harm that was different, and maybe alter the moves a bit. Still, you could use most of DW at some level.
5e, maybe not so much. I mean you could do a lot of the above, de-emphasize equipment and whatnot, but equipment feeds heavily into the rest of the rules, so that would take some work. Magic in D&D is definitely not Tolkien magic, so that would have to be addressed, which probably means scrapping or heavily revising spell lists and many/most classes and sub-classes.
The thing is, DW/PbtA DOES HAVE HOOKS, in fact in spades, to address motivations, methods, style, and such of the PCs and the kinds of threats and how they fit into the world. D&D just doesn't. It isn't like you CANNOT try to figure it out, but I think a fairly light revision of DW would inherently do it. With 5e it would be a matter of each DM figuring out for himself all of the above, and then invoking the correct rulings in the right way to get the flavor to come out right. It is not going to be a walk in the park, and the only sort of mechanical approach that I can see is an 'indie' Story Now sort of one where the game inherently introduces that flavor. No amount of simply presenting spells, classes, monster, and such in 5e fashion will get you there, the game simply lacks the 'language' needed to describe what makes Middle Earth tick.