"Unable to verify macOS" when I try installing the OS on an external SSD
The 2018 MacBook Air includes the T2 security chip which can make it so you can't install macOS on an external disk. According the Other World Computing's blog:

Unable to Install Catalina on an External Drive
This issue can occur because of the T2 Security Chip found in recent
vintage [sic] Macs. The T2 chip protects your Mac by default from being
booted from an external device. This prevents someone from walking up
to your Mac with a USB flash drive, booting your Mac, and accessing
your files.
The default settings will also prevent you from installing Catalina on
an external drive.

They go on to explain that you need to tweak some of the Startup Security Utility settings, explained on another blog post.

To open the Startup Security Utility, you must boot your Mac in
Recovery Mode. To do this:

Turn on your Mac, and immediately press and hold Command (⌘)+R
after you see the Apple logo.
Booting in Recovery Mode, the next thing you’ll see is the macOS
Utilities window. Select Utilities &gt; Startup Security Utility from
the menu bar.
You’ll be asked to authenticate; click Enter macOS Password, then
enter the name and password for an administrator account.


You would then need to set Secure Boot to No Security and set External Boot to Allow booting from external media.
Reboot your Mac and try to install the macOS on your external drive. According to everything I've read, the install should progress as expected.
Be sure to set your Startup Security Utility settings back to Full Security and Disallow booting from external media when you are done.
See also https://support.apple.com/HT208198