The 4 groups of 9 is correct, split into the last 5 years club coefficients, so effectively 2 clubs from each category of 1st, 2nd, 3rd and 4th seeds. Each club will play 2 games against ALL categories, something that doesn’t happen now, as you say, 4 home and 4 away. Those groups are created purely to determine fixtures, it will be just one league of 36 teams, there will be no tables for the 4 x 9 “groups”.
Also after the first year of the competition I’ve read somewhere the historical coefficients will be phased out and a new seeding system will replace it, think they’ll probably just go off the previous years domestic position but not really too sure about that.