Unlike Stack Overflow meta, I've noticed that here all my reputation points have been transferred over from the main site. But not badges.
Will my reputation be synced between the two? If so, why not the badges as well?
All metas work the same except Stack Overflow, which is treated like a normal site in the network because it predates Stack Exchange's expansion into many separate sites. MSO has a problem where people who post ideas can often lose rep because the idea gets voted down, even though the post itself was well written. The per-site metas avoid this problem by not having a notion of meta rep, or even meta accounts; it's just an extension of the parent site that keeps the meta posts separate from the actual Unix/Linux content. Since meta still has privileges just like the main site, we still need rep of some kind, so we use the rep of the parent account.
So in short, reputation is synced because you need reputation to use privileges here. Badges aren't synced because there's no reason for them to be; you don't need them for anything