Do note that was my complaint with $0, that when using $PATH it was set to that full gross path.
If /bin/foo is actually /nix/store/3508wrguwrgu3h5y9354rhfgw056y-foo-5.0/bin/foo, then when you run "foo", 0="/nix/store/3508wrguwrgu3h5y9354rhfgw056y-foo-5.0/bin/foo" and BASH_ARGV0="foo".
If /bin/foo is actually /nix/store/3508wrguwrgu3h5y9354rhfgw056y-foo-5.0/bin/foo, then when you run "foo", 0="/nix/store/3508wrguwrgu3h5y9354rhfgw056y-foo-5.0/bin/foo" and BASH_ARGV0="foo".