prob , PATH inheritage | early modment , sudo , wsl deb

[alex xmb sw ratchev]

i have :
wsl debian , starting that windows app brings up terminal and normal user
is logged in

i wanna do :
auto login to root , and have the from-user /mnt/c/*windows* PATHs

i did :
a login bashrc / profile that saves the extra paths to a var
and have /root/*somebashrc* add that to PATH
cause i couldnt make it neither inherit nor early-add , to PATH , BASH_ENV
nor --init-file worked

my cmdline :
sudo HOME=/root sps="${PATH#*:/bin:}" bash -l < optional args bad code >

? why only rc file in /root fix this problem ?

i had tried and failed :
a_code = printf %s\\n 'PATH+=:$sps'
sudo BASH_ENV=<( a_code ) bash -l
sudo bash --init-file <( a_code ) -l
sudo bash --init-file /dev/fd/3 3< <( a_code )

i also of course removed all bashrc profiles in /root and /etc
it always forced root sbin paths , without my :$sps additon
the $sps is filled

works : rc file in /root
 [[ $sps ]] &&
PATH+=:$sps sps=

but why no init file or bash env do
what i do wrong
what i missed

greetings , microsuxx softwāār