After successive wins, especially over Man City. I believe Klopp will continue his leadership with Liverpool, at least until the end of this season.
The defeat to Nottingham Forest in yesterday's match was very disappointing for Klopp, Klopp is still struggling to improve his squad's performance and is targeting as many wins as possible and trying to finish in the top four of the premier league.
if only Klopp was sacked at this time. a situation that will not be favorable for Liverpool, because they have a busy schedule plus want to ensure Liverpool to qualify for the next round in the champions league.
Here I agree with you, even if Klopp leaves now. it won't help Liverpool to win some trophies with its new coach.
It is difficult to talk about the dismissal of Klopp because we do not know the position of management on this issue. Maybe he has a lot of credibility, maybe not. It makes no sense to change a coach a month before the World Cup, so I think that Klopp will definitely remain in his position until the end of the World Cup + a few more games in the Premier League and the Champions League. If these games are successful then he will definitely continue to coach Liverpool, if Liverpool continue to fail (and fail in the Champions League for example) then Klopp's story at Liverpool may be over.