Please, fix the title of your post: replace
Tk with
Tkx.
It seems you think the value of the button is tied to the value of the variable, i.e. when the variable changes, the value of the button changes, too. But that's not the case, it's similar to
my $mode = 'old';
my $entry_mode = $mode;
$entry_mode = 'new';
print $mode; # Still 'old'.
You need to configure the button to change its value every time the entry changes.
($q=q:Sq=~/;[c](.)(.)/;chr(-||-|5+lengthSq)`"S|oS2"`map{chr |+ord
}map{substrSq`S_+|`|}3E|-|`7**2-3:)=~y+S|`+$1,++print+eval$q,q,a,
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