How would I explain what the older! Nyssa Arc is like? ( I know someone who is hesitant to listen to them because they don’t want Nyssa’s personality “fixed” by Big Finish)
I keep trying to write a brief answer and failing.
I’ve been a Nyssa fan pretty much since Keeper of Traken first aired in the US, and I think the older!Nyssa TARDIS has become my favorite TARDIS team. EVER.
It’s like the Nyssa of Big Finish’s Season 19b audios— Circular Time, 1001 Nights, or even Castle of Fear— came back after spending several more decades doing what she already does, and now she’s more knowledgeable (mainly about diseases, though it doesn’t come up much). Since she’s older, she’s more assertive/confident— she’s not pushy about it, she’s just not as meek, and if she’s paired off with Turlough or Tegan she’s usually subtly in the lead. Although older!Nyssa varies by scriptwriter; some don't seem to take her age into account, while others exploit the fact that she’s more experienced.
In fact, the complaint from some fans is that older!Nyssa is exactly the same as she’s always been, so what was the point? I don’t think that’s true— if nothing else, she developed a friendship with Turlough, which there wasn’t time for on TV— and it allows the writers to split the TARDIS team and still have Doctor/companion or companion/companion working together.
One aspect of older!Nyssa that does come into play— only in a few stories, but I wish it had been more— is that since part 4 of Circular Time had post-Terminus Nyssa cross timelines with the Fifth Doctor at the end of his incarnation, older!Nyssa (for whom that adventure is her past, his future) has to conceal part of her life from him which he doesn’t learn until later, to avoid paradox. That means she confides in Tegan about those things. Also, Turlough tells Nyssa a few things about himself that he did NOT tell the Doctor until his backstory came out in Planet of Fire (this only comes up in one story, Kiss of Death, but it’s a nice touch).
What’s magical about the older!Nyssa arc that it brings together four actors and characters who really work well together. Even their inevitable frictions are good character dynamics, more interesting than pointless bickering and sniping.
TL;DR: Big Finish didn’t “fix” older!Nyssa, because she didn’t need to be fixed. They just gave her better stories and more opportunities to be Nyssa, even in a crowded TARDIS. Because she’s no longer eclipsed by the more assertive, noisier characters.
The only trouble I have about the older!Nyssa arc is that towards the end (Prisoners of Fate, Entropy Plague) they heaped more angst on her shoulders, as if having her planet destroyed and the Master murder her father and then wear his body wasn’t bad enough. But how she reacts to that angst is absolutely in character, hearkening back to her actions in Keeper of Traken, Castrovalva, Arc of Infinity and her choice at the end of Terminus.
Just warn them not to listen to Rat Trap, which I believe got her character wrong in a fundamental way, but that has nothing to do with her age. Anyway, it’s icky.