It took the lessons learnt from the US invasion of Iraq and Afghanistan/Global War on Terror, and applied them

I'm not sure this is really what the Armata was doing - in a lot of ways, it was a continuation of existing Russian (inherited from the Soviets) design philosophy.

There's two aspects to the Armata program - the tank itself, and the Armata Universal Combat Platform, which is meant to be a common chassis for many different systems - tanks, artillery, APCs, IFVs, etc.. The later is an obviously appealing idea and has already been practiced in a more limited sense for a long time by both the Soviets and the West (like using existing tank or APC chassis for recovery or engineering vehicles, or self-propelled artillery). There is however an ambition to extend it further (an American example is the Future Combat Systems program), but it keeps running into the same problem - that APCs/IFVs have fundamentally different needs for their chassis than tanks, so actually uniting them would mean you either get a tank that's too lightly armed-and-armored, or APCs that are way too heavy and expensive. In the Armata's case, the T-15 IFV seems to have been even less successful, the T-14 at least did do some actual combat trials in Ukraine and was eventually withdrawn, but I'm not sure if the T-15 has been seen anywhere outside of parades. So for now at least you're kind of stuck needing at least two main tracked chassis designs (or three, if your APCs and IFVs are separate, but some countries have recently shifted to a unified chassis at least for those two classes of vehicle, like the AMPV being essentially a turretless Bradley, or the still-ongoing (and rather troubled) British Ajax program which includes both an APC and an IFV variant).

For the tank itself - I'm not sure it really is that based on GWOT experiences, beyond the inclusion of active protection (which I feel like isn't informed so much by the GWOT but by Russia's own experiences with urban counter-insurgency in Chechnya, which naturally leads to trying out ways to protect oneself from a guy with an ATGM hiding out somewhere managing to take you out; these experiences also led to the BMPT Terminator and its concept of a "tank support" vehicle, something on a tank chassis but armed more-so to fight infantry, with good optics so it can spot and quickly respond to such threats much better than a tank can), but there's nothing about the APS concept that requires the development of a whole new vehicle (and most APS systems are indeed designed as add-on upgrades), aside from perhaps a new hull/turret being able to accommodate some of the sensors better than trying to kludge them onto an existing one.

I think part of the narrative around it has been that it's more "Western" in design, but it really isn't, beyond just being expensive (and contrary to the pop-history view, the Soviets were perfectly willing to spend more on fancier equipment in certain contexts that merited it, like aircraft or nuclear submarines, and even in ground forces - the widespread fielding of autoloaders is obviously quite a technological advancement, and while Soviet tanks are generally viewed as simpler compared to Western ones, the post-T-64 designs are quite a bit more complex compared to previous Soviet designs). This perception seems to come from the propagandistic narrative of those evil Soviets who just didn't care about crew survivability, and since the Armata makes improvements on that front, it represents the Russians shifting away from the Soviet philosophy to a Western one.

But the actual main part of the Armata (and seemingly where a lot of the issues stem from) is the idea of fully-remote turret, with the crew moved to a special armored capsule in the front - and this development comes from a Soviet program that started in '88, so it definitely precedes the GWOT era. This is where that "Western design" assumption comes in again - people assume the purpose of the capsule is purely crew protection, and thus it indicates the Russians moving from the (supposed) Soviet "eh, just let 'em blow up" philosophy to the Western "every tanker is sacred" one. But if we consider this in continuity with the history of Soviet tank design, it actually seems like the natural next step in their philosophy of minimizing the volume of the crew compartment, thus minimizing the surface area that has to be protected by thicker armor, allowing you to cut weight (and cost, since you're just spending less on materials). This philosophy informed the proliferation of the autoloader, and it's that design choice which allows Soviet tanks to be so much lighter compared to Western ones - by eliminating the loader (who's the crew member needing the most space to work in, due to the wider movements required for his role), you can substantially reduce the crew compartment, which in turns allows you to make a much smaller turret, one which will be lighter by simple geometry - there's just less of it that you need to cover with armor. For example, one of the only Western MBTs to also use an autoloader - the French Leclerc - is indeed a decent bit lighter compared to the Abrams and Leopard 2 (although still heavier than the T-90), and pretty comparable to the Chinese ZTZ-99A.

So where do you go from there? Well, what if you could remove the crew from the turret altogether, and stick them in the front of the hull somehow? That way, you'd have an armored "capsule" containing just the crew, which is where most of the armor would be focused, allowing the rest of the tank to be made much lighter. That's how the Armata can be so much bigger than the T-90 while being of comparable weight - the actually heavily-armored part of the Armata is much smaller.

But the obvious problem with this is - how does the crew actually command the turret from their little capsule? Well, you need a whole bunch of sophisticated electronics and optics to make that viable - and that makes the vehicle more complex, expensive, and fragile. The tech just isn't there yet.