Problem let Frescobaldi recognize convert-ly in Lilypond 2.24.0 on macOS

[TamuraJun]

Hello list,

I’ve been running Lilypond 2.22.2 and Frescobaldi 3.2, both installed with 
MacPorts, on macOS Monterey 12.6.2. I’ve just download “official” 
lilypond-2.24.0-darwin-x86_64.tar.gz, unzip/untar it in my home directory, and 
now I have:

~/lilypond-2.24.0/

Then, in Frescobaldi, I opened Frescobaldi -> Preferences…,
selected LilyPond Preferences,
clicked +Add… for the LilyPond version to use,
specified ~/lilypond-2.24.0/bin/lilypond for LilyPond Command,
and clicked Set as Default to make the 2.24.0 as the default.

By choosing LilyPond -> Engrave, Frescobaldi runs LilyPond 2.24.0, not the 
older MacPort-installed 2.22.2., and I got anticipated syntax errors as my 
LilyPond code is written for 2.22.

Then I choose Tools -> Update with convert-ly… but I cannot find LilyPond 
2.24.0 in the pull down menu where you expect to choose the desired LilyPond 
version. I found only "LilyPond 2.22.2 (/opt/local/bin/lilypond)” in the pull 
down menu.

My understanding is that Frescobaldi would automatically look for convert-ly in 
the same directory as the LilyPond executable is located (that is 
~/lilypond-2.24.0/bin/lilypond) and there certainly exists 
~/lilypond-2.24.0/bin/convert-ly.

Am I missing something?

Thanks in advance for your help.