Agreed, - Liverpool are where Manchester City were two seasons ago, but, but but, the weight of Anfield, as you so eloquently expressed it, has been lifted to a large extent by their Champions League form over the past two years.
Two years ago, in 2018, they reached the final; last year, they won the trophy, and that, I would argue has boosted their confidence to the extent that the niggling doubts (do we bottle at the last minute, do we bottle or flake in the final stretch, or, when it matters, - yes, Steven Gerrard - and so on) are no longer moot.
Last year, they chased Manchester City in the Premier League to the very last day, losing one match all season, and failing to win the PL by one point. Manchester City could only win by being at their very best for the entre season. This is not a crisis of confidence or self-belief.
Liverpool now know that they can deliver at the highest level, and this - to my mind - has liberated them form the burdens of the histories, legacies, and traditions of the past.
And yes, of course, this is a superb team, working under an outstanding manager who have learned to win stylishly, win ugly, and win professionally as you say. But, now they also play with the confidence of knowing that they can deliver at the very highest level.
I have said all along that (barring catastrophic injury to key players) I expect Liverpool to win the Premiership this season, and they will have deserved it.