It depends on who actually is supposed to change the text. If only the user should change the text, instead of referencing the variable directly I would use the events on the<FocusOut> event to update the value in $mockOb manually:

 
my $mockOb = SomeClass->new;

my $search = $contentFrame->new_ttk__entry(-takefocus => 1, -font => '
+Arial 11', -width => 40, -validate => 'focusout',  -textvariable =>\$
+mockOb->search, -validatecommand  => [\&searchValidation, Tkx::Ev('%P
+')]
);

# Write information back to our $mockOb
$search->bind('<FocusOut>', sub { $mockOb->search( $search->value )});

sub searchValidation{
....do crazy stuff
}

SomeClass
sub new {
    my $class = shift;
    my $self = {    
            search = ""
    };
        
    bless $self, $class;
    return $self;
}

sub search{
    my $self = shift();
    if(@_) {
        $self->{search} = shift();
    }
    return $self->{search};
}
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But I haven't done Tk for a long time, so I don't know how applicable my idea of handling the focus event is, and if it is actually done the way that I wrote above untested code.