MacBook Air 11", Early 2015, MacOS 10.15.2 update error

Perhaps if the MacBook /Air were started in Safe mode, and after you'd login to get going

there; it then would be enough to simply restart normally to have the macOS update finish.

• Use Safe mode to isolate issues with your Mac - Apple Support

https://support.apple.com/en-us/HT201262

This usually has an effect on problematic issues, even when simply done; and it could help.

Try it from here, this site uses a different server:

Download macOS Catalina 10.15.2 Update

You need to clear more space, 10 GB isn't enough. You need a minimum of 3X the space of the download to actually install and a lot more than that for the OS and other apps to run efficiently.

A good rule of thumb is not to let your hard disk storage drop below 10-15% free space.