How can I bring this gaming PC build under ₹2 lakh?

There is no serious compatibility issue apparent, but the graphics card is the weaker part relative to the CPU. If you do not plan a future upgrade, choosing a slightly cheaper CPU and redirecting the savings to the GPU would create a more balanced gaming build. Also compare prices for equivalent 32GB DDR5 kits and SSDs, since those components can vary considerably between stores.

The overall parts list is solid, but the RAM and case look like possible places to cut costs. DDR5-6000 is the important target; CL36 is generally fine if it is substantially cheaper than CL30, especially if that allows you to keep a 2x16GB kit. You could also consider a less expensive airflow-focused case. The current cooler should be adequate for the selected processors, so adding a second CPU cooler would not make sense.

The build is weighted more toward the CPU than the GPU. A Ryzen 5 7500F, Ryzen 5 7600/X, or Ryzen 5 9600X should still perform very well for gaming. The money saved could go toward a stronger graphics card, such as an RX 9070-class model, which would usually provide a bigger gaming-performance improvement than keeping the 7800X3D with the current GPU.

You can probably save a noticeable amount on the SSD. Less expensive PCIe 4.0 drives from brands such as Patriot, SanDisk, or Lexar should load Windows and games similarly in normal use. For a gaming-focused system, paying a premium for a high-end SSD usually does not translate into much extra performance.