Re Coutinho, maybe in his early years he was a bit in and out but the last 2 and half years he was unreal. For somebody that was more a midfielder than a forward, his goal and assist rate was insanely good. What you could say regarding Coutinho is that he didn't really have a position in a Klopp side.He reminds me of Coutinho, who also never sold me at Liverpool. If play wasn't going through Coutinho, he was out of the game (both offensively and defensively). Diaz obviously has a much better defensive workrate, but I don't think he offers enough in an attacking sense when play isn't run straight through him, and for a player reliant on getting the ball and being the main man, a goal or assist every game and a half isn't enough.
To be clear, I'm setting high standards - the point I made is that I'm not sold on him replacing Mane, which is something very few players are capable of doing. Diaz is an excellent footballer and I'm very glad we have him, but he's far from the automatic pick that Mane was and I don't think that I necessarily rank him ahead of Jota/Darwin/Gakpo in that role.
On Diaz, if you're basing this on Mane 2016 to 2020 then I agree. Mane was out of this world in that period and it would be hard for any forward to reach that level however 2021 onwards he was not nearly the same player, which is why he was getting left out fairly regularly for Jota and then Diaz when he arrived. Whether Diaz can reach Mane 2016-2020 level only time will tell but the early signs, for me at least, are really promising. I don't think you can make direct comparisons between the two as I think they're different players and I also think moving forwards we're going to play slightly differently to how we play now. I think moving forwards we're going to play a 4-2-3-1 or some sort of variation of that and that suits Diaz down to the ground. He is much more of a traditional winger than Mane (or Salah) was. Mane and Salah are very much out and out forwards who start from wide positions - they're game is about playing on the shoulder of the last defender and making runs in behind or diagonals into the box. Diaz still makes those forward runs but he plays a lot wider and carries the ball a lot more. I actually couldn't agree less with you on the point about how much influence he has on the game compared to Mane - I think he has far more influence on the game and I'm not saying that as a criticism of Mane, I think it's normal because of the role he plays is different. I'm sure I wrote this before but my one criticism of Diaz was that he doesn't score/assist more based on how much he was influencing games.
As above, I don't think you can make direct comparisons between the two as they're slightly different players and I think Diaz is going to end up playing more of a wide midfield role rather than a wide forward role moving forwards but in terms of their influence and importance to the team, I think Diaz is (or at least was before his injury) well on the way to reaching the sort of levels Mane reached. His defensive output was the best we've had from any wide attacker under Klopp, his position means he gets on the ball more often in deeper positions and still he wasn't far off reaching players like Mane's attacking output (Mane averaged a goal or assist every 128 minutes during his time at Liverpool to Diaz's 140).