I'd go with moritz's solution and simply use Digest::SHA1::sha1_base64(), but just in case you want to know why your attempt didn't work, here's why:

    $sha->add(@ascii);
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should've been

    $sha->add(encode_utf8($x));
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You just need to add the (UTF-8) string itself, not a list of stringified byte values such as "112", "97", "115"...  (i.e. you did compute the digest of the string "11297115115119111114100").

Also, in your Java code, you're printing out the digest as signed bytes. To get the same behaviour in Perl, you'd need to

    @z = unpack("c*",$sha->digest);
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which would then print out as expected (when adding spaces for better readability (print "@z\n") ):

91 -86 97 -28 -55 -71 63 63 6 -126 37 11 108 -8 51 27 126 -26 -113 -40
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import java.io.UnsupportedEncodingException;
import java.security.MessageDigest;
import java.security.NoSuchAlgorithmException;
import sun.misc.BASE64Encoder;

public class enc{

public static void main(String[] args){

    String plaintext = "password";
    MessageDigest md = null;

    try
    {
      md = MessageDigest.getInstance("SHA"); 
    }
    catch(NoSuchAlgorithmException e)
    {
      System.exit(1);
    }

    try
    {
      //Encoding into UTF-8 
      System.out.print("UTF-8 : ");
      for(byte b : plaintext.getBytes("UTF-8")){
        System.out.print(b);
      } System.out.println();
      md.update(plaintext.getBytes("UTF-8")); 

    }
    catch(UnsupportedEncodingException e)
    {
      System.exit(1);
    }

    byte raw[] = md.digest(); 
    System.out.print("Encrypted Bytes : ");
    for(byte b : raw){
        System.out.print(b);
     } System.out.println();

    
    String hash = (new BASE64Encoder()).encode(raw); 
    System.out.println("Encoded: " + hash);
}}
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use Digest::SHA;
use utf8;
no utf8;
use MIME::Base64 qw(encode_base64 decode_base64);

        $x = "password";
        utf8::encode($x);
    
        @ascii = unpack("C*", $x);
        print "UTF-8 : ";
        foreach $val (@ascii) {
            print $val;                 
        } print "\n";

        $sha = Digest::SHA->new;
        $sha->add(@ascii);
        
        @z = unpack("C*",$sha->digest);
        print "Encrypted Bytes : ";
        foreach $val (@z) {
            print $val;                 
        } print "\n";
        
        #$x = "jsmith";
        #utf8::encode($x);
        #
        #print "0. \t\t" . $x . "\n";
        
        
        #Encrypt, into bytes
        #@y = $sha->digest;
        #print "1. \t\t" . $y . "\n";
        
        #Encode
        #$z = encode_base64($y);
        #print "2. \t\t" . $z . "\n";
        
        #Print
        #print "Needs to be: \t5yfRRkrhJDbomacm2lsvEdg4GyY=";
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