This is so well articulated, and (imo) spot-on with a lot of food for thought that I'm really excited to chew on—thank you, @chainofclovers, and I hope you don't mind me adding a little bit to this with one other aspect that I feel may have been in play here on top of everything already outlined.
There are the very explicit—and understandable—reasons that Deborah made this choice, as discussed in so many places: control, the triumph of being on top and not wanting to risk the legacy she finally feels secure about, vanity, etc. All totally real, particularly factoring in the reality that when Deborah does feel out of control, her instinctive reaction tends towards fear (even if it often shows up as anger and/or cruelty—s1 finale, s3 finale, much of s4, etc). That all makes sense to me.
However, I also saw a lot of parallels to the s2 finale in this episode: Deborah making an executive decision that she knows will hurt Ava but that she feels is for the best. That was obviously different in the sense that her choice in s2 was explicitly her making a choice about Ava's life based on what Deborah thought was best vs. Deborah making a choice about her life that she knows will upset Ava, but the way Jean played the moment at the restaurant when Deborah first tells Ava about her diagnosis reminded me very, very strongly of the rooftop firing scene. Riding high, celebratory, and then a notable shift from their usual ease and laughter to Deborah looking away, bracing, and very clinically and dispassionately delivering shocking and painful news that she knows Ava will fight her on. In s2, firing Ava was very explicitly about not tying her down and feeling like she had so many opportunities ahead of her; already, Deborah knew that Ava wouldn't take advantage of them because Ava would be prioritizing Deborah.
By season five, and in this context specifically, Ava prioritizing Deborah looks vastly different. And we see that immediately! In the span of minutes they go from discussing Ava's new show and this incredible new chapter of her career to Ava unhesitatingly committing herself to accompanying Deborah to every appointment, managing her meds, and being by Deborah's side every step of the way. I think it's very reasonable to imagine that at least one factor in Deborah's decision was the same need she felt in season two: to not hold Ava back.
It’s also easy to believe that their experience in Singapore underscored this idea; we know she still feels some shame around that, and I think at this stage Deborah probably views that time as Ava giving up everything for what ended up being eight months of Ava trying to hold Deborah together while she spiraled and deteriorated. It feels quite possible that Deborah was able to rationalize her assisted dying decision as a selfless act to her loved ones, most especially Ava, even if—as in season two—she knew that in the moment that wouldn't land.
Given that there are a lot of selfish* considerations in play—including very reasonable ones like not wanting to suffer, not wanting to lose control of her body, vanity, etc.— I really can imagine Deborah trying not to dwell on those but instead hold tightly to the idea that this is the right thing not just for her but also for Ava. The story she tells about her friend Gino highlights both sides of that: the grief Deborah holds for his memory being polluted by his illness, and not wanting Ava to experience that, as well as Deborah not wanting to experience something like that or risk that being Ava’s memory of her. Especially at this stage, when Deborah has secured her legacy on basically every front—best show of her career, breaking records, the Who’s Making Dinner? spinoff safe in Ava’s hands, the establishment of The Diva—the only legacy that she has left to worry about is what her legacy will be to Ava. She wants it to be Paris, and laughter, and the very best of her vs. a painful illness and deterioration that Deborah knows Ava will be there for every moment of.
*(using "selfish" as a neutral term with the understanding that bodily autonomy is in many ways an inherently selfish concept while also being an absolute human right.)
Of course, she changed her mind. @chainofclovers did such a great job of speaking to Deborah's potential thought process both in terms of making her original decision and then changing her mind, so I won't dwell, but I agree that the train station shift was in large part due to "every moment they've spent in Paris [...] still accumulating within her." The laughter, the dancing, their little world of two, but also putting back the salt and pepper shakers, Ava shouting at her for being selfish, the sheer devastation.
The actual moment of decision was wonderful, both because she lives another day (thank GOD, I was not doing well!) but also because I do think that the decision to live was, in many ways, the decision that Deborah would see as the selfish one vs. a concession she's making. As said above, she makes the decision in a moment of joy and desire for more. She also makes that decision knowing that it means a hard path not just for her, but for Ava, too, because there’s no version of this path that doesn’t involve Ava’s life being upended and her prioritizing Deborah over her career and everything else yet again. The fact that Ava would never make any other choice doesn’t change the fact that Deborah may have complicated feelings about this, but beautifully, selfishly, and rightly, she decides to not only live and fight, but also to keep Ava tied to her vs. any concept of letting her go. Which really is beautiful, because Deborah is a selfish person. She always has been! For both of them, more time with each other in the context of Deborah's illness—and, of course, more time to create art together—is the selfish choice, even if surrounded by other considerations.
And this decision was wonderfully influenced by Ava even outside of Ava’s pleading. Deborah was originally taking what she considered the easier path; she chose the option that gave her the greatest amount of control, which for Deborah is almost always a sign that she’s making a decision out of fear. Making the harder, scarier choice out of hope and trust and love is absolutely reflective of Ava’s influence on her, as it has been through the whole series from her new hour at the end of s1 to quitting Late Night.
And still—she makes her choice, knowing that Ava made hers long ago, and for the first time ever they’re getting to create together just for fun. No mountain to climb, no enemy to overcome, no worry about ratings or corporate politics. Just the two of them running around in their own little playground. Is it selfish to want that, knowing what it may cost Ava? Is it incredibly selfless, choosing to suffer rather than leave Ava? Deborah and Ava would probably have different answers to that, and I think they’re both right.