OK keeping in mind here that I think we are all largely on the same page but we're debating the "best" way to explain the issue in the world of 2022 among non-specialists:
I don't think I would agree that tranquility is a "necessary" condition.
If what we are talking about is "defining the best life" then yes it would be a significant part of the conceptual definition and in that sense it be necessary to include it somewhere in the definition of what to shoot for.
But if what we are talking about is explaining to real people a real working approximation of what we should work for at all times, then I think we would have to consider that there are times when "tranquility" is not an immediate focus, any more than many other pleasures are the immediate focus.
Getting back to the "natural and necessary" desires perspective, I would say it makes sense to include "the basics of life" (what we talk about as "necessary") as a necessary part of the goal an Epicurean would generally expect to secure at all times. But "tranquility" is often not available, as in wartime or in many other situations where energetic action is needed ( EG Epicurus diving into the stream to rescue the others in A Few Days In Athens).
Now I sense that will be responded to by the "hard cases make bad law" objection, but in this case I don't think that most of us live in a world where we can expect to be "tranquil" all the time.
To me the better way to articulate the goal in basic terms that are difficult to misunderstand is something more like:
"Life is about intelligently pursuing pleasure and avoiding pain in a way that ends up maximizing for you the pleasures of life, among which tranquility is an important pleasure along with many others."
But formulations that imply that tranquility is dominant or even "necessary" are the slippery slope to living in the cave. Some people can't achieve tranquility in the near term, but that does not mean they are any less Epicurean in pursuing the best mix of pleasure and pain that is available for them at any particular place or time.