Original author's edit note: My original answer below is now outdated. Please see @KenvixZure's answer for information on how to do this in the latest Windows 10 release. I'm leaving this answer here for historical purposes (and at the request of the question-poster).
Sometimes "negative" answers ("no") are unfortunately the only answer. While we can always hope that someone has a workaround, I don't believe that's likely to be the case.
It seems this menu option was removed on Windows 10 from the current terminals. Probably in order to leave as a special feature of Windows 11.
Not really, no. Those Windows changes in Windows 10 Insider weren't "removed". Windows 10 Insider was the staging ground for what became Windows 11. Based on that, it's completely expected that new features will only be available in Windows 11 going forward. I don't expect Microsoft (or any developer) to backport new features to old releases.
And no, you can't run one of the old Windows 10 Insider builds, as they expire.
Additional info:
The feature was first made available in some Windows 10 Insider builds coupled, of course, with Windows Terminal preview builds. There are two parts to the feature:
- The Windows/COM interface changes needed to allow a different terminal to be set as default.
- The implementation of a terminal that can implement the COM server necessary to act as the default.
In theory, it's possible to make changes to any terminal under Windows (ConEmu, Alacritty, etc.) to allow it to be set as default, but as I mention in this answer, the COM implementation needed is quite difficult.