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.