QUESTIONS/CONCERNS
"Is this some new OS, or a Linux distro?" "What is it based on?
Solus is an independently developed OS/distribution built from scratch, offering four DE's - Budgie (also independently developed from scratch), GNOME, MATE or KDE Plasma. Unlike most Linux distributions, Solus is not based on earlier Linux distributions such as Debian, Ubuntu, Arch and so on.
Solus can be characterized as either a "operating system" or a "Linux distro", I suppose, but I suspect that "neither/both" might be a more accurate characterization. Solus, as I understand it, takes the core Linux operating system and reorganizes it conceptually to a greater or lesser extent, and that is why I think "neither/both" is appropriate. As Ikey Doherty put it in a 2019 interview: "The whole thing is going to be about merging streams, so conceptually we’ll be building in a completely different way, and at that point it stops being a distribution. A distribution is exactly what it says on the tin: it’s a loosely organised, badly interconnected set of packages, and you kind of hope that they all stick in the same place when they land."
Nomenclature aside, I think of Solus as an extremely efficient implementation of Linux, much as I think of Clear Linux, which also reorganizes the Linux core.
"Is it compatible with Linux?"
I'm not quite sure what you are asking about when you ask "Is it compatible with Linux?" Solus is a Linux implemenation, but it is not based on earlier implementations such as Debian, Ubuntu, Arch and so on. As a result, users can't simply plug .deb or .rpm software packages not included in the Solus repository directly into Solus; software packages not included in the Solus repository need to be converted to .eopkg or installed as a Snap or Flatpack.
"What is the relationship with the Budgie DE?"
Like Solus itself, the Budgie DE was developed from scratch, with the goal of creating (again in the words of Ikey Doherty) "a modern take on the traditional desktop, but not too traditional". Solus and Budgie, more or less, developed together. Budgie, I suspect, is one of the reasons that Linux users are initially attracted to Solus, and, more importantly, one of the reasons that Solus users tend to stick. As I understand it, the Budgie desktop is the most popular Solus desktop, by far.
Budgie is clean, minimal and intuitive, in my opinion, and (having been a Linux user for close to 15 years, mostly Ubuntu) I have yet to find another DE that is as intuitive and internally consistent.
Budgie seems to be tightly integrated with Solus. I base that observation of having tested non-Solus implementations of the Budgie desktop (such as Ubuntu Budgie), which, for the most part, seem to be almost crayon-like in design by comparison, with more than a few rough edges and performance issues. Josh Strobl is largely responsible for Solus Budgie, and the implementation is (again in my opinion) brilliant; Budgie gets better with every iteration. It is a delight to use.
"The homepage goes on to mention bundled software. That to me is not really a differentiator - I can install the software I prefer myself ..."
Solus is a targeted distribution. Solus is intended exclusively for use on personal computers and does not include software that is only useful in enterprise or server environments. The bundled software is a curated selection; we all can quibble with this or that selection, this or that inclusion or exclusion, but the software selected seems to me to be a well-chosen selection for an end-user desktop environment on personal computers.
Because Solus is targeted, Solus does not drag around a lot of dead-weight, and that, I suspect, is one of the reasons that Solus is known to be fast and solid.
"... and the bundled versions of applications like LibreOffice tend to be old anyway (the asterisk at the end of "Shipping with the latest version of the free LibreOffice*" made me further suspect that) ..."
Solus uses a curated (that is, updates are released only after testing stable Linux and software releases, and integration into the way that Solus implements Linux) rolling release model, usually updated on Fridays, with periodic version releases (e.g. Solus 4 to 4.1, Solus 4.1 to 4.2, and so on) available for download and fresh installation. As a result of the curated rolling release model, bundled software deployed in Solus at any given time is usually the current stable version of the software and stays that way week-by-week, month-by-month, year-by-year.
BOTTOM LINE
Solus Budgie is as close to an intuitive Linux environment as I've seen.
I used Ubuntu for close to a decade, and I've used other distros (e.g. Kali) for specific projects from time to time. Several years ago, increasingly unhappy with Ubuntu's design philosophy and frustrated with the dead weight that Ubuntu seems to carry with it, I went looking. I checked out various distros (Manjaro, Mint, MX Linux, Zorin, and so on), and, although each had strengths, non "spoke" to me.
I eventually tried Solus Budgie, and I've never looked back. I still run Ubunto 20.10 in a Gnome Box to test Microsoft Edge for Linux, and I am reminded, every time that I fire up Ubuntu, that I have no reason to look back.
It seems to me that you are overthinking the problem, in a sense. Why don't you just try Solus Budgie for a while and see what you think?
