A model-independent Gray tensor product for $(\mathrm{\infty },2)$-categories

We construct a (lax) Gray tensor product of $(\mathrm{\infty },2)$-categories and characterize it via a model-independent universal property. Namely, it is the unique monoidal biclosed structure on the $\mathrm{\infty }$-category of $(\mathrm{\infty },2)$-categories which agrees with the classical Gray tensor product of strict 2-categories when restricted to the Gray cubes (i.e. the Gray tensor powers $[1{]}^{\otimes n}$ of the arrow category).