moving to a new computer with updated ios

Use the last Time Machine backup from Mojave to migrate everything but applications to the new MacBook Air running macOS Sonoma. You should confirm beforehand that there are no deal breaker 32-bit applications installed on Mojave (use the free Go64 app to see these), and that your printer/scanner vendor offers drivers for macOS 14.

You will want a new Time Machine backup drive formatted as APFS to use with the new Mac. I continue to use Crucial X8 SSD (1050 MB/s) for this purpose without any issues. These are USB 3.2 Gen 2 (10 Mbps) rated drives and come with a USB-C cable rated for the drive. The drives ship formatted as exFAT.

Yes, just plug it in. But you might lose some 32 bit applications like iPhoto, which won't run on the new computer.

When you buy a new Mac the easiest, quickest and most reliable method to migrate from the old Mac to the new Mac is to simply connect the old Mac's Time Machine External Hard Disk to the new Mac using a USB cable before you turn on the new Mac. You will likely need a USB A to USB C adapter, you can find them on Amazon for $10 or less. When you start the new Mac for the first time it will startup Setup Assistant (SA), SA will get to a point where it asks if you are migrating from another computer, select Yes  and follow the on-screen prompts and it's done! It is THAT simple.

If you have already done SA on the new computer then simply connect the Time Machine External Hard Disk using a USB cable and launch Migration Assistant (MA) which is located in Applications - Utilities - MA. Then follow the on-screen prompts. 

The ONLY difference between MA and SA is MA will create a new user account that you need to log into.

Both SA and MA migrate applications (not 32 bit apps), data files & settings. They do not migrate Mac OS itself. Some professional apps such as Adobe and Microsoft apps may require re-installing their apps as they will not allow them to be migrated. As long as you kept the security keys for installing their apps, it is not an issue. 

Finally, never EVER use Wi-Fi when doing Setup Assistant or Migration Assistant. Why, it simply fails in most cases. Please read and follow the directions in Setup Assistant and Migration Assistant. If you do not have a Time Machine backup of the older Mac then create one! If you are not aware of Time Machine, please read Back up your Mac with Time Machine and finally if you need an External Hard Disk to use as a Time Machine External Hard Disk then many experience users on these forums prefer the OWC Mercury Elite Pro due to it's reasonable price, high level of quality and ease of use.