I don't think flatseal isolates child processes, only the flatpak itself.

You could use firejail. That is available outside the AUR. As there is no socket available, if testing with a browser it should force the browser to crash. You could also try setting up a network namespace that only binds to loopback in case you want local device network access.

EDIT: I don't think you need to switch distros to solve this problem, but if you do you could try NixOS. Obviously there is no AUR, but you can write .nix config files to fine tune how firejail automatically works with specific applications:

programs.firejail = {
  enable = true;
  wrappedBinaries = {
    
    firefox = {
      executable = "${pkgs.firefox}/bin/firefox";
      profile = "${pkgs.firejail}/etc/firejail/firefox.profile";
      extraArgs = [
        "--private-home=.mozilla"
        "--whitelist=\${HOME}/Desktop/BrowserSandbox"
      ];
    };

    transmission-qt = {
      executable = "${pkgs.transmission-qt}/bin/transmission-qt";
      profile = "${pkgs.firejail}/etc/firejail/transmission-qt.profile";
      extraArgs = [
        "--net=none"
      ];
    };
    
  };
};