You can call
kpsewhich -var-brace-value=TEXINPUTS
and you get (reformatted adding a line break after :):
.:
<userhome>/texlive/2019/texmf-config/tex/kpsewhich//:
<userhome>/texlive/2019/texmf-var/tex/kpsewhich//:
<userhome>/texmf/tex/kpsewhich//:
!!/usr/local/texlive/texmf-local/tex/kpsewhich//:
!!/usr/local/texlive/2019/texmf-config/tex/kpsewhich//:
!!/usr/local/texlive/2019/texmf-var/tex/kpsewhich//:
!!/usr/local/texlive/2019/texmf-dist/tex/kpsewhich//:
<userhome>/texlive/2019/texmf-config/tex/generic//:
<userhome>/texlive/2019/texmf-var/tex/generic//:
<userhome>/texmf/tex/generic//:
!!/usr/local/texlive/texmf-local/tex/generic//:
!!/usr/local/texlive/2019/texmf-config/tex/generic//:
!!/usr/local/texlive/2019/texmf-var/tex/generic//:
!!/usr/local/texlive/2019/texmf-dist/tex/generic//:
<userhome>/texlive/2019/texmf-config/tex/latex//:
<userhome>/texlive/2019/texmf-var/tex/latex//:
<userhome>/texmf/tex/latex//:
!!/usr/local/texlive/texmf-local/tex/latex//:
!!/usr/local/texlive/2019/texmf-config/tex/latex//:
!!/usr/local/texlive/2019/texmf-var/tex/latex//:
!!/usr/local/texlive/2019/texmf-dist/tex/latex//:
<userhome>/texlive/2019/texmf-config/tex///:
<userhome>/texlive/2019/texmf-var/tex///:
<userhome>/texmf/tex///:
!!/usr/local/texlive/texmf-local/tex///:
!!/usr/local/texlive/2019/texmf-config/tex///:
!!/usr/local/texlive/2019/texmf-var/tex///:
!!/usr/local/texlive/2019/texmf-dist/tex///
I just masked the path to my home dir; in your case you can get <userhome>/.texlive (this is distribution dependent). A trailing // or /// means that the directory is searched recursively. A leading !! means that the (recursive) search is done by looking in a ls-R file generated by maketexlsr. Otherwise the (recursive) search is performed at runtime.
The various paths are searched in the specified order, a match will stop the search.
The first . represents the working directory when the TeX engine is called from.
texmf.cnf. – Ulrike Fischer Aug 23 '19 at 14:01kpsewhichuses a file calledls-R(inside thetexmf-distfolder) which contains a list of known files and their location inside the texmf tree. Is that what you are looking for? – Phelype Oleinik Aug 23 '19 at 17:33