And in later books when he claims that Snape “never betrayed him and was always faithful”, isn’t that totally excluding the entire first book when Snape was blatantly sabotaging his plans?
Read the Book (caps intended). Snape explains to Bellatrix at the beginning of ‘??? ? that he wasn’t aware of Quirrell being possesses, and in his own words…
“I think you next wanted to know,” he pressed on a little more loudly, for Bellatrix showed every sign of interrupting, “why I stood between the Dark Lord and the Sorcerer’s Stone. That is easily answered. He did not know whether he could trust me. He thought, like you, that I had turned from faithful Death Eater to Dumbledore’s stooge. He was in a pitiable condition, very weak, sharing the body of a mediocre wizard. He did not dare reveal himself to a former ally if that ally might turn him over to Dumbledore or the Ministry. I deeply regret that he did not trust me. He would have returned to power three years sooner. As it was, I saw only greedy and unworthy Quirrell attempting to steal the stone and, I admit, I did all I could to thwart him.”
So this neatly sums up why Voldermort didn’t contact Snape, or vice versa.