You need to consider what comes before and after the digits (\D is a non-digit):

use strict;
use warnings;

while( my $Number = <DATA> ) {
   
   chomp $Number;
   
   if($Number =~ /(\D|^)\d{1,8}(\D|$)/){
   
        print "$Number is OK\n"
   
    }
    else {
        print "$Number has more than 8 digits!\n"
    }

}

__DATA__
1234567
12345678
123456789
grunge 1234567 grunge
grunge 12345678 grunge
grunge 123456789 grunge
[download]

Gives:

1234567 is OK
12345678 is OK
123456789 has more than 8 digits!
grunge 1234567 grunge is OK
grunge 12345678 grunge is OK
grunge 123456789 grunge has more than 8 digits!
[download]