awk, if else conditional when record contains a value

I'm having trouble getting an awk if/else conditional to properly trigger when the record contains a value. Running this in zsh on Mac OS Catalina.

This script (issue is on second to last line)...

echo "abcdefgh" >  ./temp
echo "abc\"\(\"h" >> ./temp
echo "abcdefgh" >> ./temp
echo "abcde\(h" >> ./temp 

val='"\("'
key="NEW_NEW"
file="./temp"

echo $val
echo $key
echo $file

echo ""
echo "###############"
echo ""

awk '
    BEGIN { old=ARGV[1]; new=ARGV[2]; ARGV[1]=ARGV[2]=""; len=length(old) }
    ($0 ~ /old/){ s=index($0,old); print substr($0,1,s-1) new substr($0,s+len) }{ print $0 }
' $val $key $file

outputs:

"\("
NEW_NEW
./temp

###############

abcdefgh
abc"\("h
abcdefgh
abcde\(h

I want to fix the script so that it changes the "\(" to NEW_NEW but skips the parenthesis without the quotes...

"\("
NEW_NEW
./temp

###############

abcdefgh
abcNEW_NEWh
abcdefgh
abcde\(h

EDIT

This is an abbreviated version of the real script that I'm working on. The answer will need to include the variable expansions that the sample above has, in order for me to use the command in the larger script.