I don't know about that. 2016 felt like it had a more coherent story, sure it wasn't as indepth, but it was solid in its simplicity for the most part. You had to dig to get to the weird super nerd stuff.
Pretty much all the events that you list from the DLC, also happend in Doom Eternal, you had all this stuff just show up out of no where. They pretty much just ignored the story from 2016 and used the characters in a new story and threw in a bunch of new stuff that wasn't even mentioned.
I can sort of see what you're getting at, but for me, I think what you like about Doom 2016 is what I dislike about it.
Doom 2016's story is super simple - demons invade, wake up, kill demons. Anything remotely interesting is in voiceovers or in codex entries, and even then, the codex entries only really mention Argent D'Nur and the Night Sentinels right towards the end of the game. To borrow a cliche, there's a saying in writing that asks "if you're not writing about the most interesting point in your character's life, why?" From a story standpoint, all the most interesting elements of Doom 2016's story, from Argent D'Nur, to the Seraphim, to the Slayer doing all this stuff in Hell, happens prior to the game itself. Yes, I can appreciate the need for Doom to have gone back to basics at this point, but even then, this is the third time we've been on/near Mars in the series, and it's basically the same premise.
Doom Eternal however, steps things up a notch. You can argue that it doesn't link with the previous game well - we don't know how the Slayer got to the Fortress of Doom, and it's a bit iffy concerning Hayden going from "we can rebuild and use argent energy again" to leading the ARC. But even that aside, from the perspective of worldbuilding, Doom Eternal goes much, MUCH deeper into the lore of Doom, and as bonkers as it is, it does have a sense of gravitas to it. Furthermore, Doom Eternal's story doesn't have the problem of Doom 2016's, in that interesting material is happening in the present. Isn't just the Slayer saving Earth, but confronting the maykrs, the ghosts of his own past, Hayden, etc. It's a weird case where the Slayer knows more than the player (e.g. we see the Khan Maykr at the start, and have no idea who she is, even if the Slayer does), but even if you don't read the codex, you can probably get what's going on, and what's happened before.
In Doom 2016, most of the interesting stuff happened before the game, and it doesn't really inform the present - Argent D'Nur is academic to the UAC, and not really relevant to the Slayer, whose motive seems to be "hunt demons because I like killing demons." In Doom Eternal, even without saying a word bar flashbacks, we get how he came to be the way he is, why he does what he does, and why he hates Hell (and Urdak). It's why you can get a scene like this:
And have it carry a huge weight. Because even if the moment is short, there's a lot going on there. We know why the marauder hates the Slayer, we know why the Slayer hates the marauder, and even if you don't know that, just from the visuals, you can guess that:
a) The marauder has some similarities with the Doom Slayer, given the icons on his armour
b) The Slayer hates him so much that he's willing to postpone returning to the fortress, but also treats him as enough of a threat to take his time before dashing in (compared to his "peh, whatever" approach in Doom 2016)
Or at the end of the gladiator fight, when the Slayer contemptuously throws the medallion to the corrupted Night Sentinels rather than face them. Is it contempt? Or can he not bring himself to fight them? Whatever the case, these moments aren't really present in Doom 2016 - least not to the same extent. The Slayer's one of the few cases (IMO) of a silent protagonist done well, and moments like this are part of why.