In general with Linux sites with deb/rpm/etc files would usually include hashes for the genuine versions etc. Not to say the actual author of these could be malicious.

Imho, these hashes are hardly a security feature. If a malicious actor can control the file that you download, they likely can also control the hash.

Even with sandboxing, they generally need access to save files/load files etc from the host environment. Where are these connections defined? Could a malicious actor for example grant their malicious appimage/flatpak more access? Genuine questions, I’ve never looked into how these work.

Good question. I hope there's some form of security present, but I really don't know.

But in the end, the most valuable stuff on a computer is user data anyway. Who needs root on a machine, if the attacker can also encrypt all your personal files?

AppImages have no sandboxing as you said. They also rely on the deprecated SUID-root binary FUSE2. AppImages are bad for security but they are convenient. A malicious AppImage could for example connect to org.freedesktop.secrets and access your keychain, or run a script that places a script called "sudo" in $HOME/.local/share/bin that is preferred over the real sudo and logs a password, or encrypt your files in a ransomware attack, or exfiltrate your session cookies from Firefox or Chromium browsers.

Flatpaks on the other hand are sandboxed. IIRC Flatpaks can't access other Flaptak's data folders in $HOME/.var/app (maybe even if home access is given?), but if given access to the "home" permission they can read and write to anywhere else in the user home, so stealing session cookies from a browser or ransomware could still be possible given the right permission. Modern apps that are designed to work as Flatpaks can use the xdg-desktop-portal to access only specific files/dirs upon user request, but it is only temporary access to a file. All the ways a Flatpak can access the system are defined by its permissions, so by giving more/dangerous permissions (such as devices or full filesystem access) a malicious app can possibly escape the sandbox and access arbitrary permissions. The worst permission an app can have is access to session bus for org.freedesktop.Flatpak, which allows it to arbitrary permissions, host command execution, and access to Flatpak configuration.