Assuming no duplicates the following may do what you want:

use warnings;
use strict;

my @nlist = (0,1,2,3,4,5,6,8,10);
my @key_list = ('A'..'Z');
my $tolerance = 1;
my %hoa;

while (@nlist) {
    my $key = shift @key_list;
    my $previous = shift @nlist;
    
    last if ! @nlist;
    
    my $centroid = $nlist[0];
    
    @{$hoa{$key}} = ($previous) if  $previous >= $centroid - $toleranc
+e;
    
    for (@nlist) {
        last if $_ > $centroid + $tolerance;
        push @{$hoa{$key}}, $_;
    }
}

print "$_ => [@{$hoa{$_}}]\n" for sort keys %hoa;
[download]

Prints:

A => [0 1 2]
B => [1 2 3]
C => [2 3 4]
D => [3 4 5]
E => [4 5 6]
F => [5 6]
G => [8]
H => [10]
[download]