That's the beautiful part. There doesn't need to be lore and backstory and all that other bullshit if all you want is a shooty game. Just..."demons on mars/ demons on earth now" for those that just want to move from set piece to set piece. For those that like exploring every nook and cranny there's more.
I'm pretty sure it's implied that Doom & Doom II weren't fully removed from the continuity, though.
IIRC, the original games end with the Doom Marine stuck in hell... Which is also where they found the Doom Slayer. Additionally, despite his background with the Argenta, the Slayer is confirmed to be human in an audio recording; and his Praetor armor is similar enough to the UAC Elite Guard armor that he can upgrade his armor with tokens taken from dead guards.
So... In short, the Slayer might still be the Marine, but with a ton of interstitial backstory that kind of renders his actual origin irrelevant.
too focused on figuring out the gun/enemy type mechanics.
I haven't finished Eternal and would probably need to drop the difficulty to the lowest setting to try. I just can't keep up with combat that fast, especially when it feels like I have less freedom to choose my weapon than in 2016. 2016 wanted me to rip and tear, but Eternal wants me to play 3D chess while skateboarding.
2016 was perfect, and a worthy successor to the original. I think the scene in the beginning sums it up: there's a story, but doomguy doesn't care and smashes the screen. Rip and tear.
Aside from the stylistic change to ugly, cartoony visuals, and the more restrictive, rigid gun mechanics, Eternal's story was all over the place. I only got a few hours in, but it was just random characters that had nothing to do with anything.
Doom 2016 kind of felt like it hit the sweet spot between the two. Just enough lore to be interesting, but still grounded in a simple premise. Then Doom Eternal had so much lore I actually had to check that I hadn't missed a game where all this stuff had been introduced.