(UPDATED: APRIL 9, 2021) HBO Max launched May 27, 2020.
Among other offerings is a section of "classics curated by TCM" that includes about a quarter of its titles from the HBO library, a quarter from Warner Bros., and more than half from Criterion.
For the Warner Bros. library (Warner Bros./MGM/RKO): HBO Max | Warner Bros. catalog
For a list of Looney Tunes shorts: HBO Max | Looney Tunes
For a list of Popeye shorts: HBO Max | Popeye
For a list of Tom and Jerry shorts: HBO Max | Tom and Jerry
For a complete listing of available titles: HBO Max | Complete Collection