tabularx does not fill full textwidth when using ltablex

It is not clear, what is your problem. If I a little bit correct your selection of column widths (so, that their contents doesn't overlap) result is just fine:

documentclass{article}
usepackage[table,x11names]{xcolor}
usepackage{ltablex}
newcolumntype{L}{>{raggedrightarraybackslash}X}
setlengthextrarowheight{2pt}

begin{document}
    begin{tabularx}{textwidth}{|l| % <--- changed column type
                                  >{hsize=1.3hsize}L| 
                                  c| % <--- changed column type
                                  >{hsize=0.7hsize}L|}
caption{Used is texttt{ltablex} table environment}
label{my-label}    
    hline
    rowcolor{Snow2}
textbf{Nº} & textbf{Nombre de la unidad} 
                & textbf{%}   & textbf{Duración} 
    hline
UT11        & Utilización de frameworks arquitectónicos en cliente 
                & 5             & 5 sesiones        
    hline
    end{tabularx}
end{document}

I am able to reproduce the issue you mention when loading ltablex if I have the geometry package present while using your snippet.

Or using the KOMA-script documentclass{scrartcl} that also sets the geometry of the page.

In both cases it can be controlled with the command keepXColumns. From the manual:

Another feature that has been added is to treat the X columns like 'l' columns if the table contents would allow that to happen without exceeding the specified width of the table.

In other words, the specified width is treated as the maximum allowed and not the exact width of the table. This feature is the default but can be disabled (or enabled) with keepXColumns (or convertXColumns).

Geometry + tabularx

Geometry + ltablex (table is 411pt wide)

Geometry + ltablex + keepXColumns (table is 483.6pt wide = to texwidth)

Only ltablex (geometry not loaded and article class)

Only tabularx (geometry not loaded and article class)

The two last results are the same since ltables uses tabulax, but notice the vertical space added before the table by ltablex.

documentclass[12pt,a4paper]{article}

usepackage[left=2.00cm, right=2.00cm, top=2.00cm, bottom=2.00cm]{geometry}

usepackage{ltablex}

%usepackage{tabularx}

usepackage[table,x11names]{xcolor}
usepackage{showframe}

begin{document}
    
keepXColumns   % used with ltablex and geometry

noindent begin{tabularx}{textwidth}{|>{hsize=0.2hsize}X| >{hsize=2.9hsize}X | >{hsize=0.2hsize}X| >{hsize=0.7hsize}X |}
    hline
    rowcolor{Snow2}
    textbf{Nº} & textbf{Nombre de la unidad} & textbf{%} & textbf{Duración} 
    hline
    UT11 & Utilización de frameworks arquitectónicos en cliente & 5 & 5 sesiones 
    hline      
end{tabularx}
    
end{document}