We know predevelopment for Warhammer 3 started at the latest March 2018 from this blog post https://www.totalwar.com/blog/wttwo-03-18/
I acknowledge that Warhammer 3 will be bigger with more faction variety at the start than Warhammer 1 or 2 so it makes sense for more time needed. However 4 years seems a bit much.
This will be the first year since 2014 that CA has not released a new Total War Title and Rome 2 was release in 2013.
There was 16 months between Warhammer 1 release and Warhammer 2 release so they probably spent maybe a year on Warhammer 2 production. We are looking at 52 months between release of Warhammer 2 and 3 and 4 years of production. Perhaps in hindsight putting a little people onto the Warhammer "Team" would have been a better idea