Which operating system is your computer using? Do your computer have other applications or utilities (such as font manager apps) running in the background? In the past I've seen certain applications cause individual font styles to disappear in Adobe app font menus.
Sometimes simple trouble-shooting steps can properly refresh the fonts list. Try re-booting the computer to see if that helps. If that doesn't work try signing out of the Creative Cloud account, re-booting the system and then signing back into the CC account. Use the Creative Cloud Desktop App to do that. Make sure libarires are syncing in the CC desktop app. In some stubborn cases it might be necessary to delete the font data cache to force the computer to re-build it.
I tested the version of Asap at Adobe Fonts on my system running Win 11 Pro. All 8 styles work alright in Adobe Illustrator.
Asap is also available at the Google Fonts web site. You might try downloading/installing that version to see if the same error with the Medium and Semi-Bold styles occurs. It's possible for font files to have bugs; I've encountered them from time to time with fonts downloaded from the Google Fonts web site. Months later I could go back and download another copy of the type family and find the errors fixed.