I hear you, and had actually just added Tinderbox to my Christmas list. So, good to know it's worth the read.
That said, I feel like Succession actually had a pretty fast turnaround, relatively speaking, across it's first two seasons, at least. I did some quick research, and came up with this...
SEASON 1
- Filmed October 2017 through February 2018 = 5 MONTHS of filming
- Premiered June 2018 = 3 MONTHS after filming
SEASON 2
- Filmed March 2019 through July 2021 = 5 MONTHS of filming
- Premiered August 2019 = 1 MONTH after filming
SEASON 3
- Filmed November 2020 through June 2021 = 8 MONTHS of filming
- Premiered October 2021 = 3 MONTHS after filming
A few notes…
- Season three obviously took longer to film because of Covid protocols/location securing, and I doubt they were filming that entire eight months as well (in fact, it sounds like there was a fairly big gap before they filmed all the Italy stuff in May/June).
- If you throw out 2020, each season premiered two months later in the calendar year than the previous season. So, June, August, and October premieres, respectively.
- If that pattern holds, we'd be looking at a December 2022 season four premiere. That said, HBO never debuts their biggest series in December. Instead the latest in the year they debut a signature show is October (so that the season ends in December). And seeing as October '22 is likely impossible to meet (schedule-wise, and because HBO's 2022 is insanely staked already), the next slot is January '23 (almost always the second weekend in January, at that). Though, it's rare for HBO to debut big signature shows in January as well, because January through March is traditionally reserved for the first season of a new show, or an additional season of their middle tier stuff. But March has always seen the debut of a big, blockbuster season, namely for Game of Thrones, which used to almost always premiere in the spring.
-All of this is to say, it's looking like either January '23 or March '23 for season four, though I'd bet heavy on March. Gun to my head, after starting writing next month, I bet they start filming this summer into the fall, for five to six months, then season four premieres three or four months later in March '23.