The average cost per episode of STD is around $8-8.5m. Taking the average cost of an episode, doubling it because it was a feature-length two-parter and taking into account that it was the season finale, the total cost of production was likely around $20-25m(ish)
Like a big sci-fi feature, “Discovery” hasn’t been cheap: The average episode costs $8 million-$8.5 million. “It was like shooting a movie, the scale of it,” Yeoh says of making the pilot, which was directed by David Semel, who clashed with Fuller. “It wasn’t just ‘Quick, let’s get the shot. Move, move.’”
Variety: Can ‘Star Trek: Discovery’ Help CBS Boldly Go Into a Streaming Future?
Since these shows are not being filmed in sequential order (like a network show would be), but as a single monolithic entity which is released simultaneously when all of the footage garnered from their 'block shooting' has been cut into episodes, it's quite hard to point at a single episode and say "it cost x" because the cost of production is shared amongst the entire series, but certainly it was a more expensive episode than normal.
We always have a lot of meetings on Discovery. Nevertheless, Patrick Tidy (first assistant director) and I knew that due to the size of 213/214, and the fact that we were block shooting, we were going to have many, many more meetings than we were used to — on set, at lunch, and even after we’d wrapped for the day. Visual effects meetings were a big part of the load. We had endless meetings with Jason Zimmerman (VFX Supervisor) and Ante Dekovic (VFX Supervisor) about the Red Angel, space battles, and Enterprise bridge screen and wall extensions. Rob McCallum (storyboard artist) and I generated 145 pages of storyboards to help these discussions along.
The first day of shooting we overlapped with episode 212, “Through the Valley of Shadows,” which Doug Aarniokoski was directing. As a producer/director, we usually try to make sure we’ve got hyper-experienced directors we trust going before us or after us, and Doug is easily one of those guys.
Director's Log 213.214: Behind the Scenes of the Season 2 Finale