I essentially want to combine what these 2 do

• chmod: Path::Tiny supports a chmod method (e.g. $obj->chmod("0755") or $obj->chmod("a+x")), which it gets from File::chmod, unfortunately Path::Class, which you're using in your code, does not, but you can use Perl's chmod (just make sure to check for errors). Perl's chmod only supports numeric modes, though.
• cd: chdir (make sure to check for errors)
• pwd: getcwd from Cwd

As for your code, it's pretty long and I've only skimmed it for now, but one thing I noticed is that you're using ->stringfiy a lot, into temporary variables. While certainly not wrong, it's kind of cluttering up your code a bit - for debug output, you should be able to print the objects directly, and also note that it's not necessary to stringify the objects only to turn them back into objects again later. Using $srd3 as an example:

my $rd3 = dir( ... );
my $srd3 = $rd3->stringify;
mkdir $srd3 or warn "couldn't make $srd3: $!\n";
say "srd3 is $srd3";
$b = file( $srd3, $_ );
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Can be written instead as:

my $rd3 = dir( ... );
$rd3->mkpath();
say "rd3 is $rd3";
my $f = $rd3->file( $_ );
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