tcolorbox with Equation and footnotetext

As I commented, remove the footnotetext macro from the align* environment, because it performs a multiple-pass, grabbing the footnotetext on each pass.

Please let me know if I misunderstand your need.

documentclass{article}
usepackage{amsmath}
usepackage{amsfonts}
usepackage{amssymb}
usepackage[most]{tcolorbox}
begin{document}
    
begin{tcolorbox}[title=CORREÇÃO]
    A equação da corrente no emissor de $Q_1$ e $Q_2$, com $V_{BE} = V_B - V_E$     
    
    begin{align*}
    tcbhighmath{ I_{E_1} = dfrac{I_S}{infty} , e^{dfrac{(V_{B_1} - V_E)}{V_t}}   }      qquad
    tcbhighmath{ I_{E_2} = dfrac{I_S}{infty} , e^{dfrac{(V_{B_2} - V_E)}{V_t}}   }
    end{align*}
    footnotetext{Video Aula 3C, Slide 17, 9:50 minutos}
    
    Dividindo $I_{E_1}$ por $I_{E_2}$ e vice-versa:
    
end{tcolorbox}

end{document}

If your goal (I'm trying to understand the red arrows in the OP figures) is to place the footnote in the tcolorbox itself, I would instead fudge it, as I do below using stacks. In the left box, I use a tiny footnote size, and in the right box, I use scriptsize.

documentclass{article}
usepackage{amsmath}
usepackage{amsfonts}
usepackage{amssymb}
usepackage[most]{tcolorbox}
usepackage[usestackEOL]{stackengine}
stackMath
begin{document}
    
begin{tcolorbox}[title=CORREÇÃO]
    A equação da corrente no emissor de $Q_1$ e $Q_2$, com $V_{BE} = V_B - V_E$     
    
    begin{align*}
    tcbhighmath{ Shortunderstack[l]{%
    I_{E_1} = dfrac{I_S}{infty} , e^{dfrac{(V_{B_1} - V_E)}{V_t}}\
    rule{4em}{.6pt}text{tiny Video Aula 3C, Slide 17, 9:50 minutos}}} 
    qquad
    tcbhighmath{ Shortunderstack[l]{%
    I_{E_2} = dfrac{I_S}{infty} , e^{dfrac{(V_{B_2} - V_E)}{V_t}}\
    rule{4em}{.6pt}text{scriptsize Video Aula 3C, Slide 17,}
    text{scriptsize 9:50 minutos}}} 
    end{align*}
    
    Dividindo $I_{E_1}$ por $I_{E_2}$ e vice-versa:
    
end{tcolorbox}

end{document}