Problem with csquotes, greek and bibliography

I cannot seem to be able to use quotation marks correctly. I have loaded csquotes package, and I am also using ucharclasses to automatically change hyphenation rules in my text. Below you can see the MWE and the result:

Here is the MWE:

documentclass[12pt]{extarticle}

%%%Font and Languages%%%%%%%%%%%%%%%%%
usepackage{fontspec}
usepackage{csquotes}                                          % Suggested Prerequisite for babel package
setromanfont{Kerkis}
usepackage[Latin,Greek]{ucharclasses}                      % This Package allows the setTransitionTo commands, which are necessary for bilingual text
usepackage[english,greek]{babel}
setTransitionTo{BasicLatin}{hyphenrules{english}}     % Try to change hyphenation only, lighter
setTransitionTo{GreekAndCoptic}{hyphenrules{greek}}   % Change language depending on character read

%%%%Bibliography%%%%%%%%%%%%
usepackage[backend=biber]{biblatex}   
addbibresource{bibliography.bib}
usepackage{url}
urlstyle{same}
usepackage[hidelinks,unicode,colorlinks]{hyperref}
usepackage[normalem]{ulem}                                             %For Uline command below
usepackage{xcolor}
hypersetup{colorlinks,urlcolor=blue,citecolor=black,linkcolor=black}   %Make URLS blue
% %% Underline in line URLS hyperef
makeatletter
begingroup
  catcode`$=6 %
  catcode`#=12 %
  gdefhref@split$1#$2#$3$4{%
    hyper@@link{$1}{$2}{uline{$4}}% or underline
    endgroup
  }%
endgroup
 
begin{document}
subsubsection{Ελληνικά}
selectlanguage{greek}
"Ελληνικά"
 
 "English"cite{libreThermo}
 
 selectlanguage{english}
"Ελληνικά" cite{feynman1992there}
 
 "English" cite{dawon1963electric}
 
 printbibliography[title={Βιβλιογραφία}]
end{document}

You can see that when in text, no matter what language I select, the English quotation marks appear. On the other hand, in the bibliography, no matter the language, I get Greek style quotation marks.