Effectively, that code is identical to this:

use strict;
use warnings;

use 5.010;
use feature qw(say);

sub inner_sub {
    my $param = shift;
    say "Start inner_sub1";
    return ++$param;
}

sub outer_sub {
    
    say "Outer Subroutine Start ...";
    my $param = 0;
    say "PARAM: $param";
    $param = inner_sub($param);
    say "PARAM: $param";
    say "Outer Subroutine End.";

}

# Main
outer_sub();
exit(0);
__END__
[22:16:28.33] c:\test>junk41
Outer Subroutine Start ...
PARAM: 0
Start inner_sub1
PARAM: 1
Outer Subroutine End.
[download]

The fact that inner_sub() is enclosed in outer_sub() makes no difference to its visibility:

use strict;
use warnings;

use 5.010;
use feature qw(say);

sub outer_sub {

    say "Outer Subroutine Start ...";
    my $param = 0;
    say "PARAM: $param";
    $param = inner_sub($param);
    say "PARAM: $param";
    say "Outer Subroutine End.";

    sub inner_sub {
        my $param = shift;
        say "Start inner_sub1";
        return ++$param;
    }
}

# Main
outer_sub();
inner_sub(); ### Visible here also!
exit(0);
__END__
[22:20:34.37] c:\test>junk41
Outer Subroutine Start ...
PARAM: 0
Start inner_sub1
PARAM: 1
Outer Subroutine End.
Start inner_sub1
[download]

But, declaring nested sub is "dangerous" in that it can result in closures that don't work properly like this:

use strict;
use warnings;

use 5.010;
use feature qw(say);

sub outer_sub {
    my $scoped_var = 'fred'; ## closure

    say "Outer Subroutine Start ...";
    my $param = 0;
    say "PARAM: $param";
    $param = inner_sub($param);
    say "PARAM: $param";
    say "Outer Subroutine End.";

    sub inner_sub {
        my $param = shift;
        say "Start inner_sub1";
        say $scoped_var;  ## closure
        return ++$param;
    }
}

# Main
outer_sub();
inner_sub();
exit(0);
__END__
[22:22:00.66] c:\test>junk41
Variable "$scoped_var" will not stay shared at C:\test\junk41.pl line 
+20.
Outer Subroutine Start ...
PARAM: 0
Start inner_sub1
fred
PARAM: 1
Outer Subroutine End.
Start inner_sub1
fred
[download]

Though I forget the circumstances in which the "Variable "$scoped_var" will not stay shared " actually causes a problem. I think it's been possible to declare inner subs for a long time, certainly as long as I've been using Perl, but AFAIK, there is no good reason for doing so, and it can--though I forget the circumstances because I never do it--cause problems.