My understanding is that you have to tell polyglossia what font to use for each language, and when you are using each language.

Blue is FreeSerif font set as \hebrewfont.
By the time biblatex/biber reads the .bib file, the polyglossia command in the .bib file is already established, because polyglossia has been loaded before biblatex.
The dummy bib ref is just a random snippet from the Wikipedia article on the solar system.
MWE
% !TeX TS-program = lualatex
\documentclass{article}[9pt]
\begin{filecontents}[overwrite]{Midrash.bib}
@book{frenkelYvnymBvlmvHrvkhny1981a,
title = {\begin{hebrew}עיונים בעולמו הרוחני של סיפור האגדה\end{hebrew}.},
author = {Frenḳel, Yonah.},
date = {1981},
publisher = {{Hakibuts Hame'uḥad}},
location = {{Tel-Aviv}},
langid = {hebrew}
}
@book{מ,
title={\begin{hebrew}מערכת השמש\end{hebrew}},
author={\begin{hebrew}נפטון\end{hebrew}},
}
\end{filecontents}
\usepackage{reledmac}
\usepackage{xcolor}
\usepackage{fontspec}
\usepackage{polyglossia}
\usepackage{wrapfig}
\setdefaultlanguage{italian}
\setotherlanguage{hebrew}
\setmainfont{Times New Roman}
\newfontfamily\hebrewfont{FreeSerif}[Script=Hebrew,Color=blue]
\usepackage[style=verbose-trad3, doi=false,
isbn=false,
url=false,
eprint=false,
backend=biber
]{biblatex}
\addbibresource{Midrash.bib}
\Xarrangement[A]{paragraph}
\begin{document}
\section{אבגד -- without environment}
\section{\begin{hebrew}אבגד \end{hebrew} -- with environment}
\begin{hebrew}אבגד הוז חטיך כלםמ ןנסע ףפץצ קרשת\end{hebrew}
See \cite{frenkelYvnymBvlmvHrvkhny1981a,מ}
\printbibliography
\end{document}
I used biblatex's \addbibresource command, as well.
Addendum
Babel package
Lualatex can identify scripts by using Unicode algorithms, so explicit markup is not generally needed. (Multiple runs of different scripts diving in and out of the main script, like the Latin texts in the Hebrew-version bibliography, will need markup, for a tidier presentation.)
For a comparison of intermingled languages (ignoring runs), using babel package compiled with lualatex to take advantage of this feature, with Italian as the main language:

MWE
\documentclass{article}[9pt]
\begin{filecontents*}[overwrite]{\jobname.bib}
@book{frenkelYvnymBvlmvHrvkhny1981a,
title = {עיונים בעולמו הרוחני של סיפור האגדה.},
author = {Frenḳel, Yonah.},
date = {1981},
publisher = {{Hakibuts Hame'uḥad}},
location = {{Tel-Aviv}},
langid = {hebrew}
}
@book{מ,
title={מערכת השמש},
author={נפטון},
}
\end{filecontents*}
\usepackage{reledmac}
\usepackage{xcolor}
\usepackage{wrapfig}
\usepackage{fontspec}
\usepackage[italian,bidi=basic]{babel}%<--- main language
\usepackage[autostyle]{csquotes}
\babelfont{rm}{Noto Serif}
\babelfont{sf}{Noto Sans}
\babelfont{tt}{Noto Sans Mono}
\babelprovide[import, onchar=fonts ids]{hebrew}
\babelfont[hebrew]{rm}[Color=blue]{LiberationSerif}
%\makeatletter%workaround to satisfy biblatex parms - not needed
%\newtoggle{blx@lang@captions@english}
%\makeatother
\usepackage[style=verbose-trad3, doi=false,
isbn=false,
url=false,
eprint=false,
backend=biber
]{biblatex}
\addbibresource{\jobname.bib}
\Xarrangement[A]{paragraph}
\begin{document}
\section{אבגד}
אבגד הוז חטיך כלםמ ןנסע ףפץצ קרשת
The cat sat on the mat.
\section{הוז}
אבגד הוז the cat חטיך כלםמ ןנסע ףפץצ קרשת
See \cite{frenkelYvnymBvlmvHrvkhny1981a,מ}
\printbibliography
\end{document}
and with Hebrew as the main language:

MWE
\documentclass{article}[9pt]
\begin{filecontents*}[overwrite]{\jobname.bib}
@book{frenkelYvnymBvlmvHrvkhny1981a,
title = {עיונים בעולמו הרוחני של סיפור האגדה.},
author = {Frenḳel, Yonah.},
date = {1981},
publisher = {{Hakibuts Hame'uḥad}},
location = {{Tel-Aviv}},
langid = {hebrew}
}
@book{מ,
title={מערכת השמש},
author={נפטון},
}
\end{filecontents*}
\usepackage{reledmac}
\usepackage{xcolor}
\usepackage{wrapfig}
\usepackage{fontspec}
\usepackage[bidi=basic]{babel}
\usepackage[autostyle]{csquotes}
\babelfont{rm}{Noto Serif}
\babelfont{sf}{Noto Sans}
\babelfont{tt}{Noto Sans Mono}
\babelprovide[import, main, onchar=fonts ids]{hebrew}%<-- main language
\babelfont[hebrew]{rm}[Color=blue]{LiberationSerif}
\makeatletter%workaround to satisfy biblatex parms
\newtoggle{blx@lang@captions@english}
\makeatother
\usepackage[style=verbose-trad3, doi=false,
isbn=false,
url=false,
eprint=false,
backend=biber
]{biblatex}
\addbibresource{\jobname.bib}
\Xarrangement[A]{paragraph}
\begin{document}
\section{אבגד}
אבגד הוז חטיך כלםמ ןנסע ףפץצ קרשת
The cat sat on the mat.
\section{הוז}
אבגד הוז the cat חטיך כלםמ ןנסע ףפץצ קרשת
See \cite{frenkelYvnymBvlmvHrvkhny1981a,מ}
\printbibliography
\end{document}
babel? With pdfTeX, XeTeX, LuaTeX? – Javier Bezos Nov 05 '21 at 14:48\setdefaultlanguage{italian} \setotherlanguage{hebrew} \setmainfont{Times New Roman} \newfontfamily{\hebrewfont}{New Peninim MT}
– Haim Nov 05 '21 at 14:54\documentclassto\end{document}and you can add your bib file as a separate code block (use the{}button to show your code as code. – Don Hosek Nov 05 '21 at 15:01\usepackage{reledmac}
\usepackage{fontspec} \usepackage{polyglossia} \usepackage{wrapfig}
\setdefaultlanguage{italian} \setotherlanguage{hebrew} \setmainfont{Times New Roman} \newfontfamily{\hebrewfont}{New Peninim MT}
\usepackage[style=verbose-trad3, doi=false,isbn=false,url=false,eprint=false]{biblatex}
\bibliography{Midrash.bib}
\Xarrangement[A]{paragraph}
\begin{document}
see \cite{frenkelYvnymBvlmvHrvkhny1981a}
\printbibliography
\end{document}
– Haim Nov 05 '21 at 15:13\texthebrew{...}or\begin{hebrew}...\end{hebrew}to enter the bibliography title, but it did not work. – LEo Nov 05 '21 at 17:58