  We numerically investigate the stationary turbulent states of spin-1
Bose-Einstein condensates under continuous spin driving. We analyze the
entanglement entropy and magnetization correlation function to demonstrate the
isotropic nature of the intricate spin texture that is generated in the
nonequilibrium steady state. We observe a $-7/3$ power-law behavior in the
spin-dependent interaction energy spectrum. To gain further insight into the
statistical properties of the spin texture, we introduce a spin state ensemble
obtained through position projection, revealing its close resemblance to the
Haar random ensemble for spin-1 systems. We also present the probability
distribution of the spin vector magnitude in the turbulent condensate, which
can be tested in experiments. Our numerical study highlights the
characteristics of stationary turbulence in the spinor BEC system and confirms
previous experimental findings by Hong et al. [Phys. Rev. A 108, 013318
(2023)].
