$input_text =~ s/^###*\s+[^\n]+\s+(?=^##)//gsm;

##</code><code>##

## This gets stripped

## This doesn't
Because it contains this line

## More headers
blah blah

##</code><code>##

## This should not get stripped, but it does

### This should prevent it from getting stripped, but it doesn't
stuff

#### This should also not get stripped

##### But it does