I suggest to use tabularray:
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[dvipsnames,table]{xcolor}
\definecolor{light-gray}{HTML}{FFFFFF}
\definecolor{light-blue}{HTML}{EBF5FB}
\usepackage{tabularray}
\title{}
\author{}
\begin{document}
\maketitle
\begin{longtblr}[
caption = {This is a caption.},
]{
colspec={m{1.2cm} m{0.5cm} m{1cm} m{1.5cm} m{1.5cm} m{1.5cm} m{1.5cm}},
row{1}={font=\itshape},
cell{2-Z}{5-Z}={mode=math},
row{2,5-7}={bg=light-blue},
row{3-4}={bg=light-gray},
hlines
}
& Day
& Month
& Hours
& Feature 1
& Feature 2
& Feature 3\\
%-------------------------------------------------
Friday
& 5
& June
&
& A_1
& A_2
& A_3
\\
%-------------------------------------------------
\SetCell[r=2]{l} Saturday
& \SetCell[r=2]{l} 6
& \SetCell[r=2]{l} June
& 14 -- 21
& B_1
&
& B_3
\\
&
&
&
& C_1
& C_2
& C_3
\\
% -------------------------------------------------
\SetCell[r=3]{l} Sunday
& \SetCell[r=3]{l} 7
& \SetCell[r=3]{l} June
& 08 -- 10
& D_1
& D_2
& D_3
\\
&
&
& 10 -- 17
& E_1
&
& E_3
\\
&
&
&
& F_1
& F_2
& F_3
\\
% -------------------------------------------------
\end{longtblr}
\end{document}

In case you used math mode only to have the subscripts, but your cells are actually only text:
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[dvipsnames,table]{xcolor}
\definecolor{light-gray}{HTML}{FFFFFF}
\definecolor{light-blue}{HTML}{EBF5FB}
\usepackage{tabularray}
\title{}
\author{}
\begin{document}
\maketitle
\begin{longtblr}[
caption = {This is a caption.},
]{
colspec={m{1.2cm} m{0.5cm} m{1cm} m{1.5cm} m{1.5cm} m{1.5cm} m{1.5cm}},
row{1}={font=\itshape},
row{2,5-7}={bg=light-blue},
row{3-4}={bg=light-gray},
hlines
}
& Day
& Month
& Hours
& Feature 1
& Feature 2
& Feature 3\\
%-------------------------------------------------
Friday
& 5
& June
&
& A\textsubscript{1}
& A\textsubscript{2}
& A\textsubscript{3}
\\
%-------------------------------------------------
\SetCell[r=2]{l} Saturday
& \SetCell[r=2]{l} 6
& \SetCell[r=2]{l} June
& 14 -- 21
& B\textsubscript{1}
&
& B\textsubscript{3}
\\
&
&
&
& C\textsubscript{1}
& C\textsubscript{2}
& C\textsubscript{3}
\\
% -------------------------------------------------
\SetCell[r=3]{l} Sunday
& \SetCell[r=3]{l} 7
& \SetCell[r=3]{l} June
& 08 -- 10
& D\textsubscript{1}
& D\textsubscript{2}
& D\textsubscript{3}
\\
&
&
& 10 -- 17
& E\textsubscript{1}
&
& E\textsubscript{3}
\\
&
&
&
& F\textsubscript{1}
& F\textsubscript{2}
& F\textsubscript{3}
\\
% -------------------------------------------------
\end{longtblr}
\end{document}

$...$) around the words in your first row. If you want to emphasis them you could use\emph{...}instead – samcarter_is_at_topanswers.xyz Feb 17 '23 at 11:49\multirows, and I did not deepen much more this aspect... never used\raiseboxso far.. :-). In general, what I would like to achieve is exactly what I have showed at the end of my question, that I called "My desired output".. that would be my final goal.. and I am open to new solutions :-) – Ommo Feb 17 '23 at 14:48