The Dark Phoenix Saga is a story that is incredibly hard to pull off on the big screen. It's a tough format to get the same kind of massive impact that the original comic arc had, but it's also a story that is integral to the X-Men for most fans. So they keep trying and falling short. Mainly because films really don't have enough time to let the story play out the way it needs. But, I think that if Disney were willing to get experimental with conventional storytelling (and WandaVision suggests they are) they can pull it off with the right impact.
In order to allow us to connect with Jean and to really empathize with her, we need time. We need to follow her for a while. Let us see her gain her powers and struggle with them. Show her fears surrounding the instability of her powers alongside the deepening relationship with Scott. Just really let the story breath and let us get to know her and the rest of the X-Men well. The best way to do this is with a combination TV shows and movies.
Let it start out in a big summer blockbuster that finds the X-Men going off into space to help repair the M'Kraan Crystal. The introduction of the M'Kraan Crystal plays well with Phase 4's multiverse exploration, as it is the "nexus of all realties." Have Jean start as Marvel Girl, naturally, and begin to explore her powers as well as her relationship with Scott. Give the character a chance to grow and the audience a chance to get attached.
End the film with the X-Men returning to Earth only to encounter the Phoenix Force just before they begin re-entry. Give an establishing shot from inside the cockpit that shows them all staring out at it as the Blackbird shudders. At that point, cut to black for the typical MCU style credits, but keep audio on the X-Men as everything descends into chaos. Stay with the audio, but cut back and forth between the credits and quick snippets of action while the X-Men scramble to evade the entity. Keep it all very jarring and chaotic before suddenly cutting all audio as Jean calmly says "It's okay, I've got this." Cut back to action for the mid-credit stinger as we see Jean outside of the ship as the Phoenix Force consumes her. Then, a tight close-up as her eyes open before the standard scrolling credits.
Rather than follow this up with the next X-Men film, let them have a show. Give the X-Men a chance to establish the world in a longer format that lets them introduce new characters. It's a great way to give us character development without needing to focus on constant action. Let Jean learn her new powers, introduce Logan, establish the relationship with Scott and hint at the tension Logan adds to the scenario. Have the bad guys be the Brotherhood of Evil Mutants and do some standard world-building to let us see how different mutants view the rest of the world. It could be the equivalent of filler comics between major events with no massive enemy.
But then you end it with the introduction of Emma Frost and the rest of the Hellfire Club. With the Hellfire Club as a follow-up mini series that serves as the vehicle for Mastermind's corruption of Jean. The Hellfire Club could serve as a good vehicle for action and battles that don't have to be massive in scale. The movies always have to go very big because they're built as blockbusters, but the Hellfire Club and the manipulation of Jean Grey is not a story that needs to be massive, it needs to be moving. Which is something a show can do that a blockbuster action flick can't. End the show with Jean becoming Dark Phoenix and destroying Mastermind, battling the X-Men, and then leaving them all behind wondering what happened.
Finally, end it with the Dark Phoenix film. The Dark Phoenix's galactic destruction and the introduction of the Shi'ar are the perfect story for a summer blockbuster. By allowing the film to start after Dark Phoenix has already arrived means they've got more space to go really big for the finale. The film wouldn't need to shove all of the establishing exposition into the first act, it could start with the X-Men figuring out how to handle Jean and bring her back. And when we finally get to the end? Jean's execution will have the serious impact of the comics that the previous film attempts lacked. At that point, it's no longer a shoe-horned story with no emotional impact. It's the permanent death of a character that we love, who is vital to the story, and one who the audience would expect to survive.
If done right, it could be bigger than the death of Tony Stark. Because Tony had been around for everything already and had been one of the major moving forces of the MCU, but Jean was just getting started. Where he was older and tired of the whole superhero thing, Jean was young and just learning to control her powers. She had shown the ability to move the MCU the way Tony did, but then was struck down before she could really do so. Her death and the fallout of the destruction she left behind could be the compelling force of the next phase.