Took my 8 month old kitten from the east coast to the west coast a few years ago. He’s a high anxiety cat as well.
I leashed trained him so he had a harness, which is beneficial because you’ll have to take them out of the carrier through security. I didn’t use any sleepy/calming things, he didn’t do well with the tests before travel.
I used a soft carrier that could open in the top. He “had” to be under the seat during travel. But after takeoff I just put the carrier on my lap and had my hand in there so he had a familiar scent and touch.
My little guy did very well. His only accident was as soon as I got to the airport so I cleaned him up in the restroom. Use puppy pads. Bring pet friendly wipes just in case. Other than that, it was a lot easier than expected.