Yes, all the autoencoders you see used in practice have adversarial loss + MSE + perceptual loss, the VAE used with Stable Diffusion also uses KL regularization

Yes, all the autoencoders you see used in practice have adversarial loss + MSE + perceptual loss, the VAE used with Stable Diffusion also uses KL regularization, while VQGAN uses all other losses to make use of the codebook.