I haven't taken the time to read and understand your full code, but, with respect to your "## desired:" comments, the way you would make the Obj instance available within Foo::foo would be to change the first line of Obj::foo to:

my $self = $_[0];  # instead of $self = shift
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so that the Obj instance passes itself as the first parameter to Foo::foo. Then add

my $self = shift;
my $caller = shift;
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to the start of Foo::foo to get the Foo instance in $self and the invoking Obj instance in $caller. You'll then be able to reference the relevant bits of $obj as $caller->cid, $caller->dbh, etc.