The “HITMAN Legacy Pack” includes all locations and campaign missions from the previous game and will be provided to players who own HITMAN: The Full Experience, HITMAN: The Complete First Season (digital or disc) or all seven episodes individually from the previous HITMAN game. The remastering happens just because the content is being ported to the better Hitman 2 engine, it's nothing special outside of that (and thereby, not something which can be made exclusive).
Just that the ones for the first game are free and checks against what content you own, while the ones offered by Hitman 2 cover the bases but have a price tag. However, there shouldn't be any 'remastered edition' and 'non-remastered edition' distinction between the Legacy Packs provided by the two games. Otherwise, yes, you'll need to buy the GOTY Legacy Upgrade pack to get Patient Zero.
You'll get Patient Zero in the Legacy Pack if you own it already. As far as I know, the difference between the Legacy Pack (and GOTY Legacy Pack) for Hitman 1 owners and the GOTY Legacy Pack provided to Hitman 2 users is only in the Hitman 1 versions being free for Hitman 1 users.