I'm sure he has a say in what areas of the team he wants strengthened but I believe it is Sven and co who are pushing things over the line. Emery was even put in front of them during the hiring process, they are the king pins now. Things are moving quickly because of them and not necessarily Unai.
Your post should be rephrased as what a difference behaving like a proper football club makes.
He may not be calling the shots but a massive bottleneck has been removed
During key stages of his bodily development Wilshere didn’t take care of his body, the smoking and drinking were clear signs of that. You can either be a lad or a footballer nowadays - not both. Jack chose the former. He’s tried to change that with his new diet recently and seems more settled but it’s too late in his career to ever come close to the potential he once showed. He blew his chance of an amazing career and will now see it out in mediocre clubs where he will only ever show flashes of what he can really do - much like the season just gone.
Emery may not be doing the negotiating but he would have input into whether he'd want a player or not, sure scouts and others might suggest someone but then he'd decide if he wanted them or not, he also probably made suggestions himself.
Nothing wrong with others suggesting potential signings to be honest, probably better than one person doing all the donkey work, just as long as the manager has the final say that is.
He probably won’t have the final say as that’s rarely how sporting directors work. He’s been given the title of Head Coach specifically. It’s probably a system he’s used to working in, especially after his time at PSG. Look at Klopp, he didn’t even want Salah but he got him and the rest is history.
Fair enough, like someone said above, he perhaps targets the areas and they come back with options. Sometimes he’ll have final say, other times not I’d imagine. Only success will give him more say in the long run I’d imagine.
I would imagine Emery would be consulted regarding the general kind of player/s that the first team is lacking (e.g GK, CB, DM with X, X and X attributes), but it will be up to Sven to come up with the list of candidates. Emery may then get to have a say on who he would pick from that list (and may get a veto, if there's anyone, but he'll have sod all to do with the recruitment process.
And really that's exactly how it should be - the club should be making long-term hires for the club, not signing players who are bound a the coach who could be gone at any moment. The players (and the backroom ream and the academy) are the constants, and with each new first team coach that comes in the club absorbs new ideas and keeps growing and evolving.
Jesus, the editing on that last post was shocking! It wasn't me though - I blame the tools! It was the android phone, and the stupid train with the stupid narrow seats and no shoulder room!