The actual type of play on words is called paraprosdokian. Where the in this case punchline is surprising in a way that makes you reinterpret the setup.
In this case "I wanna be supportive but," is kind of priming the reader to expect they're gonna say some transphobic shit then you read "fucking Mildred?" and those expectations are subverted by the actual point being essentially "Why you taking names from 2000's obituaries?"
To my knowledge there's not like a widespread name for this as like a comedic genre because it's just one of the basic ways you can structure a joke. I've seen some comics call it a swerve or an anti-climax but nothing widespread.
It's never been more true.
There are only two sexualities, Straight and Woke. There are only two ethnicities, White and Woke. There are only two genders, Male and Woke.It would almost be amusing how baby-brained these chuds' understanding of the world is were it not for the massive amount of harm they cause. Like how every accusation is a confession so it takes very little thought to work out what they think from what they accuse others of.
"They just say everything they don't like is Hitler." = Everything I don't like is Woke. "Trans people are going to attack cis women in the restroom." = That's what I'd do with unrestricted access to the women's restroom. And on, and on, and on...