I'd just like to add, Tom Petersen, has been in a few videos discussing Xe2 Battlemage in Lunar Lake. In these talks he goes on about improvements and what caused issues/bottlenecks in the previous alchemist architecture.
One thing I often hear him mention, is the change in the vector unit (the Xe core, the main computational foundation building block of Intel's render slice, is composed of two things, a vector and matrix unit). The move from going SIMD8 to SIMD16 within the vector unit apparently made significant improvements not just resolving bugs within games but also improving overall efficiency. Apparently, most games are designed for SIMD16 pipelines (because that was the industry standard that both ATI and Nvidia settled on decades ago). SIMD stands for single instruction multiple data, btw. Moving towards a higher degree of SIMD improves game compatibility. Many games have certain SIMD preferences.
They also were emulating certain instructions via software. One such example is one called execute indirect, which is used in many (modern / next generation) game engines to accelerate command lists. In Xe2, this instruction is implemented directly within the hardware itself.
I don't think there's any single reason to simply explain why current intel graphics is so bad. It's more graphics is complicated. It was Intel's first real attempt at making a larger GPUs geared towards serious graphic workloads. And there were just many short comings both from hardware, software and just generally speaking game code not being tested / optimized for their stack doesn't help either. (Chicken and egg problem, they've limited market share so game dev studios don't bother trying as they've limited amount of resources and time aswell) Overcoming these obstacles time, both of which Nvidia and AMD have had decades of. And yes, I'm aware intel has been making graphics for equally as long and have made multiple previous attempts. But Xe was fairly recent and a completely different architecture with drivers from scratch. Just look at how much Qualcomm is struggling with their adreno drivers on windows laptops.