I'm considering moving from SnapRAID to unRAID because it has real-time parity generation. However, I am very scared of silent data corruption. Is there any plugin or anything I can install on unRAID that gives me checksums that I can use to recover from SDC?

You can use btrfs as default filesystem, it checksums all files, or use xfs and a plugin, like Dynamix file integrity.

Can I adjust how often btrfs scrubs?

You can create a cron job or use the users scripts plugin.

Does BTRFS scrub automatically by default?

No, cheksums are checked on normal reads, i.e., if you're watching a movie or copying a file and the checksum fails you'll get and EIO error and it's logged on the syslog, so you'll know something is wrong, you can also schedule monthly scrubs using cron or the user scripts plugin.