[Sorry for the long response. I wanted to condense it more, but I gotta get some sleep.]
1) Item management:
Here's the biggest difference between item management in RE4 versus the more classic REs and its a big one. The storage box. While RE4 asked its players to essentially play a mini game of tetris there was never a moment where I felt pressured to make any difficult choices on do I take THIS and then that means I might not have it for later, or do I take THIS and hope that my choice as I progress doesn't come back to royally screw me.
I often found myself discarding items to make room in my inventory, as well as running out of ammo during my first couple playthroughs of RE4. This is especially apparent early in the game when you have the smallest briefcase. However, unlike classic RE games were you have a MASSIVE surplus to stash away in item boxes after the first half of the game, RE4 requires you to only hold as much as your briefcase can hold. This leads to difficult choices like selling the TMP to make room for a rifle.
Case in point? Making chemical mixes to create the different types of grenade ammo. That was vitally important in the more classic RE games, there was a real survival tension to it, because you knew that whatever choice you ended up picking was A) limited and B) Meant you no longer had the option to create the other type of ammo. Not to mention that this meant sacrificing an important inventory slot. The same applied to other types of ammo too.
Grenade ammo crafting is only in RE3. The other classic games don't have it.
So I objectively say your completly wrong when you say RE4 has more item inventory management then RE CV and I'm assuming you'd also throw RE0 into that too. That's simply not true.
Code Veronica is, imo, the most superficial RE game. It has backtracking, but doesn't have a map designed for it. It has "item management", but you are immediately given 10 slots so it's never a problem. It has puzzles, but they, in my opinion, aren't very creative. There certainly isn't a sense of horror or dread in that game, unless you get that feeling because the game is such a boring slog to get through. Haha

The game's tone has more in common with a soap opera than a horror, honestly.
RE Zero has a big focus on item management; probably the biggest in the series, but is it done well? In an attempt to freshen things up, Capcom removed the item boxes. RE4 also did this, but did it better. With Zero, it just makes the game more tedious. The game gains nothing from you having to lug the hookshot from the train to the laster segments of the game. I think it's obvious that Capcom was really struggling to keep the old style of RE fresh at this point.
**More on that later**
Puzzles. RE4 hardly had proper puzzles and you know it, what puzzle beats REmakes sunlight puzzle with the glass windows and the crows? What puzzle in RE4 made you have to really think? RECV had that type of puzzle in the first ten minutes of the game.
REmake is the best game in the series, and its puzzles are mostly great. The entire mansion is basically one big puzzle, and that is obviously the biggest focus of that game.
RE2 Classic hardly has any puzzles in comparison (to REmake or RE1), and the ones that are there don't require much thought at all. RE4 has more puzzles, and I would say they are more fun to solve. I particularly enjoy the 4 paintings puzzle, the church light puzzle, and the optional graveyard puzzle. Does this mean RE2 isn't a real RE game?
Yes Fatal Frame was different, but the design choice, the survival horror elements all share a commonality with the more classic REs, a sense of dread and fighting to survive. THAT design choice will never get old and it worked incredibly well for many years and still does.
Well, I'd say that easily describes RE4 many, many memorable set pieces--opening village segmemt, the cabin shootout, being chased by Verdugo, anything with the Regenerators, the Bella Sisters, being trapped in the prison with Garrador, etc.
I mean, RE4 probably captures that better than any other RE game to date--it's all about survival. You really think Code Veronica gives a sense of dread and makes you feel like your fighting to survive?
RE4 was a mistake, it's design choices absolutely crippled Capcom and it's choices to make it more action and more cheese was not the right direction. It let go of the classic elements of RE, puzzles, survival, tension and horror. Capcom themselves see this, as is evidenced in RE7, RE2 remake and RE8. RE3 remake tried going back to more action and got blasted for it however its far more in line with the earlier REs then RE4 ever could hope to be.
RE4 plays a lot different that the games before it, but it didn't throw away puzzles, and it certainly didn't ignore survival, tension or horror. It upped the action, of course, which is the direction the series had been going since the opening of RE2. Specific design choices, like now allowing Leon to move and shoot were made a focal point for the combat to create tension. Like the original RE games, positioning, shooting, and running to a new position before getting attacks is still the foundation of the combat.
Now for the **more on that later** part:
Around the time of REZero and CV, the series was in a bad state. Not just finically, but Capcom employees were requesting being moved out of RE projects because they were bored working on the same formula. I think this lack of passion or fresh ideas is very apparent in CV and Zero. On top of that, Capcom was going to shitcan the series if RE4 wasn't successful. RE4 objectively saved the series from going the way of Silent Hill.
You say that RE7 and RE2R are evidence that Capcom knows RE4 was a mistake, but that's like saying that RE4 is evidence that Capcom thinks RE1 was a mistake. Like how classic RE got stale and needed to change with RE4, the action RE games got stale (and quite terrible with RE6), and RE7 was an opportunity to freshen up the series again. That's just was series have to do to stay alive when they are going on this long, and I'm quite grateful that there is pretty much an RE game for any type of game. RE8 seems to be another big shift for the series, but I'm ready for it!