Zanatic To sum up the alternatives, this is the status of Edge-Linux Stable on Solus as I understand it at this point:
(1) Edge-Linux Stable was released by Microsoft this week. Microsoft offers Edge-Linux in .deb and .rpm, which align with the package formats used by Microsoft's enterprise/business partners (Canonical, SUSE, RedHat and so on), but which leave Arch-based and independent distributions (e.g. Solus) out in the cold. Microsoft has declined (based on the best information available to me at this time) to wrap Edge-Linux as a Flatpak. Microsoft's attitude toward eventual release of a Snap is unknown, although more likely a Snap than a Flatpak because Snaps are pushed by Canonical, a Linux partner of Microsoft.
(2) A community-based project is in the process of wrapping Edge-Linux as a Flatpak, with the goal of including Edge-Linux Stable in the Flathub stable channel going forward. The project is stalled at this point because of an upstream issue involving both Edge-Linx and Chrome. I don't know when that issue will be resolved, so I don't know when Edge-Linux Stable is likely to be released into the Flathub stable channel. A Github discussion of the issue is ongoing. The project developer will post developments in that discucssion.
(3) Edge-Linux is available in BETA on Flathub's beta channel through the community-based project at this point, and will continue to be available until Edge-Linux Stable is released into the Flathub stable channel. Anyone who wants to install Edge-Linux Beta can do so following the steps in this tutorial. My experience with the Beta version over the last six months is that Edge-Linux Beta is very stable, running without issues internally, although some Solus functionality (e.g. the ability to pin the app) is not available using the Flathub beta channel.
(4) It is possible to install Edge-Linux Stable locally using algent's technique described above, or by packaging Edge-Linux Stable as a private .eopkg in a local repository for your personal, private use only. If you elect to develop a private .eopkg, please do not publish or distribute the package on this forum because doing so may embroil Solus in licensing issues. Both "roll-your-own" solutions will require a level of expertise to set up an maintain, and both will entail frequent manual updating as Edge-Linux Stable releases become available every few weeks.
I think those are the only alternatives at this time. For what it is worth, I intend to continue to use Edge-Linux Beta via the Flathub beta channel on Solus until the Stable version is released to the Flathub stable channel.