Recently installed Linux Mint and long time Ubuntu/Xubuntu user.
Never used flatpak, hardly any snap, only debian (not on Arch) and appimage.
I’d check the folder you use for your Obsidian folder and obsidian config folder (.config) for root privileges. Obsidian needs user, non-root privileges, at least for the vault location, that is for sure.
Cannot think of anything else as a solid reason.