Does this exist: flatpak-like sand-boxing with gentoo-like source-based package management?

I've seen NixPak which I think would be just what you want, except that it's for Nix instead of Gentoo. But Nix has the same features that you say you like in Gentoo.

At that point you might as well use a Docker type container in which to build your software from source and deploy in the container.

Does Guix fit your criteria, perhaps? If you haven't heard of it, you can think of it as Nix with a Lisp frontend.

I unfortunately am not very experienced with containerizing packages so I can't say much, but I know you can do it; the Nonguix channel employs containers for some proprietary software.

Like Nix, Guix has all that building-from-source stuff you'd want from Gentoo. There's recently been work on making parameterized packages (the Guix equivalent of USE flags) a thing, but it's still work-in-progress.

Ignoring the steep upfront cost of learning it, I'd say Guix makes it incredibly easy to add your own packages. Here's the custom packages I currently have in my dotfiles repository. I can import one to my main config file, add the package, and it gets included in my environment the next time I reconfigure it.

As for patches, I can't make any comparisons since I'm not familiar with Gentoo, so I think a code snippet is probably better for you to judge if you'd like it.

(define-public custom-pkg
  (package
    (inherit pkg)
    (name "custom-pkg")
    (version (package-version pkg))
    (source (origin
              (inherit (package-source pkg))
              (patches
               (list (string-append (dirname (current-filename))
                                    "/fix-some-thing.patch")))))))

(define-public custom-pkg
  (package-with-patches
   pkg
   (list (string-append (dirname (current-filename))
                        "/fix-some-thing.patch"))))

Not sure if this addresses your concern about multi-architecture support, but the Foreign Architectures section of the manual discusses what you can build to.

EDIT: So I was curious after posting this because usually the CLI often has much less verbose options (like --with-input for replacing inputs), and I started wondering if there was any procedure that would make this simpler. Turns out there is :) I've included it under the example. Although, I suppose I should have mentioned you could write your own if you really wanted to.

If you're willing to spend the time to learn how to write custom policies, SELinux can be used for this, to some extent. It's highly customizable and can sandbox your apps, but the process of doing so is quite complicated. I wrote a small guide on custom policy management on Gentoo in another comment if you're interested.

There's also apparently a "sandbox" feature, but I don't know much about it. I just write my own policies and make them as strict as possible.

As an example, my web browser can't access my home directory or anything except its own directories, and nobody (including my own user), except root and a few select processes (gpg, gpg-agent, git, pass) can access my gnupg directory.

This only covers security/permissions, and doesn't include many of the other benefits of containerization or isolation. You could also try KVM with libvirt and Gentoo VMs; that works pretty well (despite update times) and I did that for a while with some success.

How about not changing at all your regular packages,and containerizing what you want, or as much as possible through current profiles, through firejail? And couplet that with MAC protection offered by apparmor (one can actually set firejail to always use apparmor, and then tweak particular apps not to use it if it's too troublesome).

This way you have your provided distro packages (gentoo or sourcemage if source based distros, it doesn't matter), and have them execute containerized. The only thing is that there are not firejail profiles for every possible piece of SW, but the vanilla list of containers is not small either.

I think it should be possible to use bwrap to sandbox programs.

Would running gentoo in a distrobox container work for you?

Build everything you use in podman or lxc