Dude. You can't betray something you never promised to support. Eddington swore an oath to Starfleet, hence he betrayed it. On the other hand, Sisko never swore an oath or made a promise to support the Maquis, so he never betrayed them.
Hunting them like rapid dogs would be simply killing them as expeditiously as possible. The Federation didn't do that either.
Instead the Federation would have happily found a garden spot planet or two and moved them there. (I think most of the settlers probably took that offer, we just didn't see them on the screen.) Sometimes people have to be resettled with some degree of coercion. Israel occupied the Sinai for a long time and part of the peace agreement with Egypt was returning the Sinai and evacuating the settlers. There have been towns in areas to be flooded by dams that had to be evacuated. When British India was partitioned into India and Pakistan, many Hindus in Pakistan moved to India and many Muslims in India moved to Pakistan, over 14 million people migrated. It's unpleasant, but better than making war against their country, with little to no chance of success.
