Do I need to disable compression on my swap subvolume?
https://wiki.archlinux.org/title/Btrfs#Swap_file
Is there anything else I should keep in mind for fstab if I want to, say, not keep track of my Downloads folder when snapshotting?
Just create a separate subvolume for it. Snapshots do not work recursively, so it will be left alone.
Mount options also only take effect on the first mount of the device. Since it looks like you only have 1 btrfs device - only /
needs the options, really.