I copy-pasted your code into Frescobaldi, added context (and initial \ for the slashedGrace) and it compiled and produced exactly what you want. Either there is a problem in your context which we're not seeing, or perhaps there is an issue with your installation. This is what I compiled:
\version "2.23.3"
{ \slashedGrace { e'8\(\downbow } <a fis'>2~<a fis'>8 <a e'>8\)--\downbow } |%m144
And this was the result:
<grace.jpg>
Paul
What I would like to accomplish is to add a phrasing slur like the one in the picture. On lilypond /frescobaldi I does not allows it (error) when I tried the code I sent.
slashedGrace { e8\(\downbow } <a, fis'>2~<a fis'>8 <a e'>8\)--\downbow |%m144
It says Error 11