There shouldn’t be any issues with that. Most distros handle “install side by side” situations out of the box.
Data partition probably doesn’t matter. Nobara might use snapshots for updates so you can rollback, not sure, but it also shouldn’t horribly break things for /home
.
The thing btrfs does well is root and home can be the same partition, but different subvolumes. Technically you can even have multiple distros on a single btrfs partition by means of subvolumes, so there’s no unusable wasted space.
I would do btrfs, Mint won’t care about the filesystem having more features than it needs, and there’s so many advantages to btrfs.
E: I might leave homes separated and explicitly share some folders you want to keep in sync. Mint’s configurations could impact Nobara’s configurations and vice-versa. Especially if versions of things differ, maybe Nobara will upgrade some configs and make them unusable with older packages from Mint. You can just symlink your downloads and documents and whatever to a common shared data partition or subvolume dedicated to that use case.
Flatseal: well that’s normal, it can’t control Flatpak’s access controls if it is itself sandboxed. Even if it was sandboxes, it could just grant itself everything.
For Xournal: it’s probably because it doesn’t support portals or whatever, so it can’t use the open file dialog to get permissions. So it needs to be able to get to your files somehow to open them.
In both cases, it just means its permissions model is more like regular applications you’d get from your package manager. If you install Xournal with apt/dnf/pacman it also won’t be sandboxed.
The point of sandboxing is you can run applications you don’t trust too much, or significantly reduce the blast radius if say, your browser gets breached: then it has another barrier to overcome to reach anything other than the browser’s own data. The lack of sandboxing doesn’t inherently imply the app is evil or will hack you. It just means it doesn’t have the extra protection around it. So like, probably don’t open sketchy PDFs in it, but I wouldn’t stop using the app solely because it lacks sandboxing.