Text formatting relative to environment (theorems)

I’ve gotten the code below from another post and, I’m not sure whether or not this is possible but, I would like to define an alternate myemph command whose effect would depend on the theorem environment in which it is embedded.

documentclass[a4paper]{article}    
usepackage{amsthm,eso-pic,thmtools,framed}
usepackage{lipsum}

    definecolor{localblue}{RGB}{55, 115, 180}
    definecolor{localgreen}{RGB}{80, 140, 30}

newcommand{myemph}[1]{emph{textcolor{localblue}{#1}}}
newcommand{miemph}[1]{emph{textcolor{localgreen}{#1}}}


    colorlet{headcolordefn}{localblue}
    colorlet{rulecolordefn}{localblue}
    newenvironment{leftbardefn}{%
        defFrameCommand{{color{rulecolordefn}vrule width 3pt} hspace{10pt}}%
        MakeFramed {advancehsize-width FrameRestore}}%
        {endMakeFramed}
        declaretheoremstyle[
          headfont=sffamilybfseries,%
          notefont=sffamilybfseries,%
          notebraces={}{},%
          headpunct=,%
          bodyfont=,%
          headformat=color{headcolordefn}NAME~NUMBERhfillNOTEsmallskiplinebreak,%
          preheadhook=begin{leftbardefn},
          postfoothook=end{leftbardefn},%
                           ]{customDefinition}
declaretheorem[
               title=Definition,style=customDefinition, numberwithin=section
               ]{defn}



    colorlet{headcolorthm}{localgreen}
    colorlet{rulecolorthm}{localgreen}
    newenvironment{leftbarthm}{%
        defFrameCommand{{color{rulecolorthm}vrule width 3pt} hspace{10pt}}%
        MakeFramed {advancehsize-width FrameRestore}}%
        {endMakeFramed}
        declaretheoremstyle[
        headfont=sffamilybfseries,%
        notefont=sffamilybfseries,%
        notebraces={}{},%
        headpunct=,%
        bodyfont=,%
        headformat=color{headcolorthm}NAME~NUMBERhfillNOTEsmallskiplinebreak,%
        preheadhook=begin{leftbarthm},
        postfoothook=end{leftbarthm},%
                         ]{customTheorem}
declaretheorem[
               title=Theorem,style=customTheorem, numberwithin=section, sibling=defn
               ]{thrm}

 
begin{document}
lipsum[2]

            begin{defn}[object]
                Such-and-such is said to be an myemph{object} when so-and-so is verified.
            end{defn}
lipsum[2]
            begin{thrm}[of the day]
                If such-and-such miemph{conditions} are met, then we're happy.
            end{thrm}
lipsum[2]

end{document}

I’ve got a series of different ‘theorem’ styles with specific colors, and I would for my command to color the text relative to the one defined in the style, e.g. I’d like it to render

with the previous code. Is there anyway to accomplish this without too many headaches?

EDIT:
as required in the comments, I modified the example to provide a more detailed one. It renders:

So my question really is: is there a way to merge the myemph and miemph commands into one (there are of course more environments than those two: propositions, corollaries…)?

documentclass[a4paper]{article}    
usepackage{amsthm,eso-pic,thmtools,framed}
usepackage{lipsum}

    definecolor{localblue}{RGB}{55, 115, 180}
    definecolor{localgreen}{RGB}{80, 140, 30}

    newenvironment{thm@leftbar}{%
        defFrameCommand{{color{thm@theme}vrule width 3pt} hspace{10pt}}%
        MakeFramed {advancehsize-width FrameRestore}}%
        {endMakeFramed}
    declaretheoremstyle[
          headfont=sffamilybfseries,%
          notefont=sffamilybfseries,%
          notebraces={}{},%
          headpunct=,%
          bodyfont=,%
          headformat=color{thm@theme}NAME~NUMBERhfillNOTEsmallskiplinebreak,%
          preheadhook=begin{thm@leftbar},
          postfoothook=end{thm@leftbar},%
                           ]{thm@custom}
declaretheorem[
               title=Definition,style=thm@custom, numberwithin=section
               ]{defn}
declaretheorem[
               title=Theorem,style=thm@custom, numberwithin=section, sibling=defn
               ]{thrm}

% since latex2e 2020-10-01
% for older latex2e, load etoolbox package
AtBeginEnvironment{defn}{colorlet{thm@theme}{localblue}thmemph}
AtBeginEnvironment{thrm}{colorlet{thm@theme}{localgreen}thmemph}

% since latex2e 2020-02-02
newcommandthmemph{%
  DeclareEmphSequence{itshapecolor{thm@theme}}}

begin{document}
lipsum[2]

            begin{defn}[object]
                Such-and-such is said to be an emph{object} when so-and-so is verified.
            end{defn}
lipsum[2]
            begin{thrm}[of the day]
                If such-and-such emph{conditions} are met, then we're happy.
            end{thrm}
lipsum[2]

test verb|emph| emph{outside thm-like envs}
end{document}