Hello vivienne200,
Welcome to Apple Support Communities. If we're understanding you right, colors in screenshots appear distorted when opening them in Adobe Illustrator after AirDropping them from your iPhone to your Mac.
Since the photos appear as expected in Preview, this issue could be related to how Illustrator is handling the files rather than a problem with your iPhone or Mac, even though you didn't experience this issue with your last iPhone. We recommend restarting Illustrator, testing it out, and then restarting your Mac and testing it again.
After that, make sure both your Mac and Adobe Illustrator are fully updated.
Screenshots are saved as PNG files instead of HEIC like photos taken with your iPhone, or JPG like you would expect to see in the Photos app on your Mac. One thing you may want to try is opening the screenshot in Preview and exporting it to a different file format before opening it in Illustrator. You can do this by selecting File > Export.
Saving the files to a different format may help narrow things down a bit, however, ultimately your best bet may be to get in touch with Adobe if you continue to experience issues.
Cheers.