Read it line by line, but keep track of which section you're in and if the section hasn't change, just concatenate. Then, when the section changes, go ahead and process the last section, then set the current section to the new one.

my ($section, @value);
while (<FILE>) {
    chomp;
    my ( $temp_section, $temp_value ) = /^(?:([^:]+):)?\s*(.*)/;

    if ( $temp_section ) {
        if ( $section ) {
            # Process the old value somehow.
        }
        $section = $temp_section;
        @value = ( $temp_value );
    }
    else {
        push @value, $temp_value;
    }
}
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