This works, but is maybe not as effective as it could be:

my @sorted = sort { $a->{total_rate} <=> $b->{total_rate} } @array;

@sorted = 
(
  (grep {     defined $_->{vtype_ug} } @sorted), 
  (grep { not defined $_->{vtype_ug} } @sorted)
);
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Note that the round brackets here are necessary.

Update:
Another way:

my @sorted = 
    map  { $_->{total_rate} *= -1 if $_->{vtype_ug}; $_ }
    sort { $a->{total_rate} <=> $b->{total_rate} }
    map  { $_->{total_rate} *= -1 if $_->{vtype_ug}; $_ }
    @array
;
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