It's interesting to look at what different TSMC fabrication processes achieved when comparing Intel, AMD and Nvidia graphics cards:
https://www.techpowerup.com/gpu-specs/arc-a750.c3929
https://www.techpowerup.com/gpu-specs/geforce-rtx-4090.c3889
https://www.techpowerup.com/gpu-specs/radeon-rx-7900-xtx.c3941
Intel's Alchemist GPUs have transistor densities of 53.4 million transistors per mm², using TSMC's 6nm fab. process. This is similar to what we saw from last generation RDNA2 and Ampere GPUs.
'Ampere Next' GPUs have transistor densities upto 125.5 million transistors per mm² using TSMC's 4nm fab process.
RDNA3 achieved the highest transistor densities on the GCD itself, with transistor densities of 150.2 million transistors per mm² using TSMC's 5nm fab process.
If Intel's Arc Battlemage GPUs use either the 'Intel 4' or 'Intel 20A' fabrication processes, there's likely to be a huge improvement in transistor density, vs Arc gen 1 GPUs. So, Battlemage could end up being a hugely scaled up version of it's predecessor, potentially at a similar TDP of around 225w, or more if they opt to use GDDR6X. I'd guess that the 'Intel 4' process would be the more likely choice for Battlemage, as it's more likely to be ready by Q3-Q4 2024.
It's a fair bet that intel opted for TSMC's 6nm process for Alchemist GPUs, because the manufacturing cost is significantly lower, than more advanced processes like 5 and 4nm. EDIT - Intel said the decision to use an external fab. was also down to their available manufacturing capacity.