Perl 5 -pl, 109 bytes

chomp;@,=$s=$_;/((.)(?1)\2|(.)(.)\4?\3)?(??{$1?push@,,$`.$':length$s>y!!!c?$s=$_:1;0})/,$_=pop@,while@,;$_=$s

Try it online!

Speed is not great. I'd claim further "-6" from the score -- chomping is only required for the "nice" TIO's many-inputs-in-the-same-screen presentation, not for an input of a single string w/o trailing LF (the same about "-l" switch.)

More readable:

chomp;
@, = $s = $_;
/
    ( (.)(?1)\2 | (.)(.)\4?\3 )?
    (??{ 
        $1 ? push @,, $` . $'
           : length $s > y!!!c ? $s = $_ : 1;
        0
    })
/x,
$_ = pop @, while @,;
$_ = $s

Perl 5 -pl, 103 bytes

@,=$s=$_;/((.)(?1)\2|(.)(.)\4?\3)?(??{$1?push@,,$`.$':length$s>y!!!c?$s=$_:1;0})/,$_=pop@,while@,;$_=$s

Try it online!

More readable:

@, = $s = $_;
/
    ( (.)(?1)\2 | (.)(.)\4?\3 )?
    (??{ 
        $1 ? push @,, $` . $'
           : length $s > y!!!c ? $s = $_ : 1;
        0
    })
/x,
$_ = pop @, while @,;
$_ = $s

Perl 5, (non-competing) 458 bytes

$s = $_;
%seen = ();
while () {
    /
        (?>^.*?)
        ( 
            (
                (.)(?-3)\g-1|(.)(.)\g-1?\g-2 
            )
            (?{ 
                $x = substr( $_, 0, $-[2] ) . substr( $_ , $+[2] );
                unless ( $seen{ $x } ++ ) {
                    push @a, $x;
                    $s = $x if length( $s ) > length( $x )
                }
            })
        )
    /x;
    last unless @a;
    $_ = pop @a
}
$_ = $s;

Try it online!

Short version is terribly inefficient. Just for fun, this is a much faster version (approx. 1 sec for 16 "go"'s in linked TIO's input vs. 9 in the challenge's test case), which hopefully generates correct results.

Perl 5 -pl, 102 bytes

@,=$s=$_;/((.)(?1)\2|(.)(.)\4?\3)?(??{$1?push@,,$`.$':$s=~s!${\y^^.^cr}.*!$_!})/,$_=pop@,while@,;$_=$s

Try it online!

More readable:

@, = $s = $_;
/
    ( (.)(?1)\2 | (.)(.)\4?\3 )?
    (??{ 
        $1 ? push @,, $` . $'
           : $s =~ s! ${ \ y^^.^cr } .* !$_!x
    })
/x,
$_ = pop @, while @,;
$_ = $s

Perl 5 -pl, 109 bytes

chomp;@,=$s=$_;/((.)(?1)\2|(.)(.)\4?\3)?(??{$1?push@,,$`.$':length$s>y!!!c?$s=$_:1;0})/,$_=pop@,while@,;$_=$s

Try it online!

Speed is not great. I'd claim further "-6" from the score -- chomping is only required for the "nice" TIO's many-inputs-in-the-same-screen presentation, not for an input of a single string w/o trailing LF (the same about "-l" switch.)

More readable:

chomp;
@, = $s = $_;
/
    ( (.)(?1)\2 | (.)(.)\4?\3 )?
    (??{ 
        $1 ? push @,, $` . $'
           : length $s > y!!!c ? $s = $_ : 1;
        0
    })
/x,
$_ = pop @, while @,;
$_ = $s

Perl 5 -pl, 109 bytes

chomp;@,=$s=$_;/((.)(?1)\2|(.)(.)\4?\3)?(??{$1?push@,,$`.$':length$s>y!!!c?$s=$_:1;0})/,$_=pop@,while@,;$_=$s

Try it online!

Speed is not great. I'd claim further "-6" from the score -- chomping is only required for the "nice" TIO's many-inputs-in-the-same-screen presentation, not for an input of a single string w/o trailing LF (the same about "-l" switch.)

More readable:

chomp;
@, = $s = $_;
/
    ( (.)(?1)\2 | (.)(.)\4?\3 )?
    (??{ 
        $1 ? push @,, $` . $'
           : length $s > y!!!c ? $s = $_ : 1;
        0
    })
/x,
$_ = pop @, while @,;
$_ = $s

Perl 5 -pl, 102 bytes

@,=$s=$_;/((.)(?1)\2|(.)(.)\4?\3)?(??{$1?push@,,$`.$':$s=~s!${\y^^.^cr}.*!$_!})/,$_=pop@,while@,;$_=$s

Try it online!

More readable:

@, = $s = $_;
/
    ( (.)(?1)\2 | (.)(.)\4?\3 )?
    (??{ 
        $1 ? push @,, $` . $'
           : $s =~ s! ${ \ y^^.^cr } .* !$_!x
    })
/x,
$_ = pop @, while @,;
$_ = $s