brent A few thoughts:
(1) The current LTS version of UB (and the one I believe you have installed) is Ubuntu Budgie 22.04 LTS rather than 20.04 LTS. I mention that only to clarify for people who read this thread.
(2) Ubuntu Budgie uses Nemo (not Nautilus) as the file manager. The change was made in 2019.
(3) With respect to Snaps: Snaps are a Canonical product. Ubuntu is a Canonical product. Ubuntu has been increasingly incorporating Snaps into Ubuntu and Ubuntu flavors as default for several years. The debate over Snaps has been vigorous and contentious, but Snaps are a fact of life for Ubuntu users.
(4) I tend to use distros OTB, installing little software, but like all Ubuntu users have noticed, when available, a Snap is usually listed first on the software installation list for that app. Debs are usually also available, but the user has to elect/select the deb installation.
(5) I would prefer that Ubuntu's software center clearly designated which installation options on a list were Snaps and which were debs, but I don't think that the practice of not doing so is "some kind of crooked deal", any more than Solus's failure to designate which apps in the software center are KDE and which are Gnome is "some kind of crooked deal". However, the failure to do so is a byproduct of the fact that Linux distros in general seem to assume that the user is experienced at a level many "ordinary home desktop users" are not. Linux could use a bit more emphasis on "truth in labeling" in many respects, and the failure of both Solus and Ubuntu in this regard is an example.
(6) Firefox and Chrome, both of which provide official Snaps, are available only as Snaps in the Browser Ballot, in line with Ubuntu's policies. Other browsers, such as Edge, for which Microsoft does not provide an official Snap, are available only as deb installations. A few browsers in the Brower Ballot are available in both formats. In the case of Firefox and Chrome, it is possible to install a deb, but the user needs to download the deb file and install the deb file through the installer.
(7) The "unsafe" designation (if you take a moment to read the description) means that a particular app contains proprietary code that cannot be checked, and the user is warned accordingly. The designation means only what it says it means. It does not mean that the app is malicious or contains malicious code, but only that the code cannot be checked and the user assumes the risk.
(8) When I used Ubuntu Budgie 22.04 LTS, I used the "Traditional Budgie" layout to approximate the Solus Budgie layout as closely as possible. The "Traditional Budgie" layout does not use a Plank, so I can't comment on Flatpak behavior on the Plank. However, Flatpaks installed on Ubuntu Budgie 22.04 LTS, like Flatpaks installed on Solus Budgie, require a restart before the app will show up in the menus. I wonder if that is also the case for the Plank.
You are having an obviously strong negative reaction to Ubuntu. Moving from Solus to Ubuntu does take some getting used to, and you may never get to the point where you are comfortable with Ubuntu. That is for you to decide. Ubuntu Budgie 22.04 LTS is an excellent implementation of the Budgie DE layer, and that's a fact. Whether UB is a distro you will want to use is up to you.