Grant was a drunk - prior to the War. He developed a drinking problem when he was posted out West many years earlier, which cost him (directly or indirectly) his commission and his civilian business. He quit drinking before rejoining the Army for the War.
That is a neo-confederate myth.
Actually, that was anti-Grant propaganda at the time. I have seen both Union and Confederate broadsides calling him a drunk. I suppose the ones from up north were from his political enemies, who tended to be better at politics than generalship.
That is really a distortion of the facts.
Grant drank when he was lonely & depressed. It started in California, yes, but he was not a "drunk". He was a man who DRANK on OCCASION and could not handle his liquor well - he got drunk easily.
The common "Grant was a Drunk!" comments care nothing for the distinction and are designed to imply that he was incompetent, immoral, intemperate, or worse, drunk on the field. That is not true. Read any one of the reputable Grant historians (Simpson, Sampson, Perret, McPherson) and they all agree on this.
I will agree with you that many of his Northern political allies also had a hand in this myth, but it was always necessary for Grant's star to fall in order for Lee's to rise in the years between 1890 and 1930 when the "Lost Cause Myth" hit full stride.