Mohammed Salah's special treatment at Liverpool isn't something that came from nowhere. He deservedly earned the king's treatment he's been getting at Liverpool because of scintillating performances he's delivered as a Liverpool player.
Before Salah's arrival, Liverpool hadn't won the English Premier League for over two decades and last won the UEFA Champions League in 2006 but after he arrived at the club, he changed the club's status quo by winning the English Top Flight since it was renamed as the English Premier League and also helping the team to European Cup glory
Mohamed Salah is one of Liverpool's brightest stars and has done so much for the club, so it is only natural that he will receive special treatment. Before Mohamed Salah joined Liverpool, Liverpool did not have much success but since Mohamed Salah joined Liverpool, Liverpool has been very successful and has played the main character in winning many big matches. In the early to mid-season of the 2022-23 season, Liverpool was not in a very good position but due to the great performance of Muhammad Salah, Liverpool finished the season at number five in the points table. So it is natural for the Liverpool management to be a bit more caring towards him.
It's no wonder why Mohamed Salah's role is so important for Liverpool and I totally agree with what you said that since the arrival of Mohamed Salah to Anfield everything has changed slowly from raising the team's performance to winning various trophies. We cannot forget these great seasons, especially when with two other players, namely Firmino and Mane, Liverpool had scared all of Europe's strong teams a few seasons ago.
The squad depth that Jurgen Kloop has is indeed not arbitrary and he managed to juggle Liverpool to win the EPL title for the first time in the 19/20 season. Indeed, so far this season Liverpool have not changed much because they are experiencing a decline in performance and perhaps Mane's previous departure could not strengthen Liverpool's attack line as usual. But indeed the role of Mohamed Salah has again become a determinant of Liverpool's return to a better position. I think most Liverpool players are over 30 and soon maybe they have to regenerate before it's too late.