Experiences / Opinions about Construction Manager

Good morning everyone,

if you want to build today, you have the advantage that you can get the "all inclusive" package everywhere. (Architect, energy, site manager...)
But I am not quite sure about the usefulness of the site manager in particular.
I will simply assume quite directly that a site manager who is not paid by me will not always necessarily pursue my concerns with full commitment, but in borderline situations might rather side with the construction company than with me?!?
Who has experience with this?
Has anyone ever had the site manager removed from the financial offer? (How was the reaction of the construction company here?)
Has anyone ever had two site managers and were there any "conflicts" then?

Thank you very much...