Why do you want to generate samples? What is your goal?
Gibbs, like all MCMC algorithms, is a way to generate samples from a target distribution whose probability density function is unknown. It might be good to look into some resources that explains the fundamentals of these methods? I like the Statistical Rethinking series.
In your case, the target distribution is known. Under some conditions, discrete markov chains converge to a stationary distribution \psi that solves the equation \psi(I - P)= 0. See here for details. In your case, this distribution is [0.14188124, 0.39936942, 0.45874934]. So without doing any simulation at all, I can tell you that the share of samples in state 2 for a chain of sufficiently long length will be about 45%.