Siar–Keskin bounded-exponent conjecture for $(a^n-2)(b^n-2)=x^2$

Let $a,b,n,x$ be natural numbers with

$$2<a<b.$$

Consider the exponential Diophantine equation

$$(a^n-2)(b^n-2)=x^2.$$

Siar–Keskin's bounded-exponent conjecture. If this equation has a solution $n,x$, then

$$n\leq 6.$$

The conjecture concerns a uniform bound on the exponent in this family of exponential Diophantine equations. The source gives no proof or resolution, so the claim remains open.