I really don't know the requirements for your application.
I have taken an imperfect attempt at it below.

I did come close to your output for "s." but not exactly.
My output for "a." is wildly off from what you show.

I downloaded your DB file to a local file to make my testing faster.
I don't think that makes any difference.

I would like more text to describe what you want to have happen.

#!/usr/bin/perl

use strict;
use warnings;

my @words;
open my $fh, '<', 'EuroScrabbleWordList.txt' or die "can't open word l
+ist $!";

foreach (<$fh>) 
{
    tr/\r\n//d;     
    tr/A-Z/a-z/;            
    next if /\s/; # dirty way of removing comments 
    push @words, $_;
}

close $fh;


############################################
my $tiles = 'a.';
# print all words with 2 letters that contain "a"
print "\nMATCHES FOR: $tiles\n";
my @m = find_matches($tiles);
print "\n@m\n";

$tiles = 's.';
# print all words with 2 letters that contain "s"
print "\nMATCHES FOR: $tiles\n";
@m = find_matches($tiles);
print "\n@m\n";

$tiles = 'a.a';
#print all words with letters that contain 2 a's
print "\nMATCHES FOR: $tiles\n";
@m = find_matches($tiles);
print "\n@m\n";


############################################
sub find_matches 
{
    my $pattern = shift;
    my $max_chars = length $pattern;
    
    my @matches;
    
    $pattern =~ s/\W+//g; #delete the dots
    my $raw_letters = $pattern;
         
    my $regex = "";
    $regex .= "[$raw_letters].?" for (1..length $raw_letters);
    print "$regex\n";
    
    foreach my $word (@words)
    {
       next if (length ($word) > $max_chars);
       
       push (@matches, $word) if $word =~ /$regex/;
    }
   
    return @matches;
}

__END__
MATCHES FOR: a.
[a].?

aa ab ad ae ag ah ai al am an ar as at aw ax ay ba da ea fa ha ja ka l
+a ma na pa ta ya za

MATCHES FOR: s.
[s].?

as es is os sh si so st us

MATCHES FOR: a.a
[aa].?[aa].?

aa aah aal aas aba aga aha aia aka ala ama ana aua ava awa baa caa faa
+ maa
[download]

UPDATE:
I don't claim that my code is a general solution to your problem.
In fact, I think that many enhancements are necessary! This was just minimal code to answer some simple questions.

In terms of algorithms, let's start with something simple:
for "s.":

You say: as es is os sh si so
I say:   as es is os sh si so st us
[download]

I am completely unable to understand why st and us should be missing from the output? Please explain.

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