Kile system check failure


I set up a native TeX Live environment on my laptop as described in the Arch wiki. In particular I followed the quickinstall guide, the only thing I changed from the default settings was the installation directory. I installed Tex Live inside my home, and I updated my environment variables inside my ~/.bashrc file as indicated by the install script:

export MANPATH="/home/giacomo/texlive/2023/texmf-dist/doc/man:$MANPATH"
export INFOPATH="/home/giacomo/texlive/2023/texmf-dist/doc/info:$INFOPATH"
export PATH="/home/giacomo/texlive/2023/bin/x86_64-linux:$PATH"

Since I’m using KDE, I decided to try out Kile, but when I run its system check wizard, I get the following results:

[Here I originally added multiple pictures showing the full output, but since I’m a new user I can only post one. The other test that fails is for PDFLaTex, but it says it’s not critical. But it would be nice to get that working as well]

A strange thing is that, even if it says it found a tool, the path is wrong:

$ which latex
$ which pdflatex

How can I fix this or further investigate the issue? The system check output isn’t that helpful in finding out what went wrong, as there is no indication of what “Simple Test” is. As a side note, it would also be convenient to be able to copy&paste the tool’s output instead of having to resort to screenshots.
Thank you for your help,