What would be the canon status of such productions?
Since it's not directly from CBS, that would essentially make it a licensed production like any other tie-in; although since it's from the other co-producers of the TV shows, the studio CBS subcontracts to make them, I'd say the closest analogy would be something like Sony's non-Spider-Man Marvel movies like
Venom or
Morbius, something from the licensed subcontractor without the direct participation of the owner. Either that or TAS before Paramount acquired ownership of it, when it was a production of Filmation Associates and Norway Corporation that was simply distributed by Paramount, which is part of the reason Paramount was cagey about acknowledging it back then.
My expectation would be that it's not canonical, or at best is canon-adjacent. But I hardly see how it matters, since I doubt any future canonical work is likely to cover or address the same subject matter and either affirm or contradict it. Of course, canon works are always free to borrow ideas from non-canonical tie-ins, like
Star Wars has done with a bunch of characters, planets, and species from the old Expanded Universe. And conversely, canon works are always free to contradict previous canon, like how TNG and
Voyager ignored how quickly the
Enterprise was able to reach the galactic center in ST V. So really, whether something is canon or not has no real impact one way or the other.
Thinking about it for a few hours, I realize that Big Finish would not necessarily be the company I would want to go with. They have produced some great drama, the War Doctor stories being especially strong, and it attracts good talent, including those who played the Doctor before. However, it floods the market with product that appears on the whole to be lower quality.
I have a similar concern. They've done some good stuff, but they do seem to prioritize quantity over quality.
Also, I suppose it might be harder for a British production to get hold of enough Trek actors who live and work in North America.
Khan only has two screen actors and an otherwise new cast, but future audios might make more use of returning regulars. I wondered if maybe they might want to limit the number of regulars they use for reasons of budget, but Naveen Andrews and Wrenn Schmidt are pretty high-profile actors.