RMO 2023 K5

The side lengths $a,b,c$ of a triangle $ABC$ are positive integers. Let:

$$T_{n}=(a+b+c)^{2n}-(a-b+c)^{2n}-(a+b-c)^{2n}+(a-b-c)^{2n}$$

for any positive integer $n$ . If $\frac{T_{2}}{2T_{1}}=2023$ and $a>b>c$ , determine all possible perimeters of the triangle $ABC$ .