Why is there an extra vertical space in Example 2

Don't use primitive tex boxes in vertical mode, they rarely do what you expect.

documentclass{article}

usepackage[most]{tcolorbox}
usepackage{showframe}
usepackage{harmony}

newtcolorbox{myFrame}
{colback = red, colframe = white, top = 0mm, bottom = 0mm, boxrule = 0pt, left = 2mm, right = 2mm}

newcommand{easy}{%
    leavevmodellap{parbox[t][0pt]{1.7cm}{%
            leavevmodeAcht{}test
            small{}easy
    }}%
}
newcommand{easyBis}{%
    leavevmodellap{parbox[t][0pt]{1.7cm}{%
            test
            small{}easy
    }}%
}

begin{document}
    
    begin{myFrame}
        easy
        Example 1par
        This is the text of the exercise.par
        By the way, I use tcolorbox to make my boxes.
    end{myFrame}
    

    begin{myFrame}
        easyBis
        Example 2par
        This is the text of the exercise.par
        By the way, I use tcolorbox to make my boxes.
    end{myFrame}
    
end{document}

or better, also hiding the height of note to get the same space above Example

documentclass{article}

usepackage[most]{tcolorbox}
usepackage{showframe}
usepackage{harmony}

newtcolorbox{myFrame}
{colback = red, colframe = white, top = 0mm, bottom = 0mm, boxrule = 0pt, left = 2mm, right = 2mm}

newcommand{easy}{%
    leavevmodellap{parbox[t][0pt]{1.7cm}{%
            leavevmodestrutsmash{Acht}test
            small{}easy
    }}%
}
newcommand{easyBis}{%
    leavevmodestrutllap{parbox[t][0pt]{1.7cm}{%
            test
            small{}easy
    }}%
}

begin{document}
    
    begin{myFrame}
        easy
        Example 1par
        This is the text of the exercise.par
        By the way, I use tcolorbox to make my boxes.
    end{myFrame}
    

    begin{myFrame}
        easyBis
        Example 2par
        This is the text of the exercise.par
        By the way, I use tcolorbox to make my boxes.
    end{myFrame}
    
end{document}