Let's start with the 2019 Mac, it is the only one that is Sonoma compatible. Is the installer sitting in your Applications folder? If it is, restart the Mac holding the shift key. Remove the installer from the Applications folder, and restart again.
Now let's make sure you understand the difference between upgrade and update.
Sonoma is an Upgrade to Ventura, is an upgrade to Monterey, is an upgrade to Big Sur, is an upgrade to Catalina, is an upgrade to Mojave (10.14.6 is a version of Mojave you mentioned).
Updates are intermediate security patches offered between the annual release of upgrades typically happening in the fall northern hemisphere.
Apple security releases - Apple Support
Covers the individual security patches to the upgrades.
If you are having trouble getting your MacBook AIr from some earlier version of Sonoma to the latest, there could be insufficient space on your Mac. Always keep at least 55 GB free if you have 128 GB of built-in storage, and 80 GB free if you have 256 GB of space. With the latest Mac OS releases you want at least 40 GB of space + 15% free.
These numbers are arbitrary based in part on the specs and in part based on seeing when swap files overwhelm the system.