Automator- Search for string of dates in title, replace them

This should do it,

In the Run Shell Script action, Pass input: [as arguments] and use:

for f in "$@"
do
    name=${f##*/}
    name=${name%.*}
    path=${f%/*}
    ext=${f##*.}
    newname=$( echo "$name" | sed -E -e 's/[._]/ /g' -e 's/[0-9]{4}$/\(&\)/' )
    newname="$newname.$ext"
    if [[ "${f##*/}" != "$newname" ]]; then
        mv "$f" "$path/$newname" 
    fi
done

This is a bit tighter for the Run Shell Script Action:

for f in "$@"
do
    basename=${f##*/}
    path=${f%/*}
    ext=${f##*.}
    name=${basename%.*}
    newname=$( echo "$name" | sed -E -e 's/[._]/ /g' -e 's/[0-9]{4}$/\(&\)/' )
    if [[ "${f##*/}" != "$newname.$ext" ]]; then
        mv "$f" "$path/$newname.$ext"
    fi
done

BTW, this also gets rid of dots and underscores, if you no longer need that, then just change:

newname=$( echo "$name" | sed -E -e 's/[._]/ /g' -e 's/[0-9]{4}$/\(&\)/' )

to:

newname=$( echo "$name" | sed -E 's/[0-9]{4}$/\(&\)/' )

...it seems like you have 0-9 in a group of 4, gets parenthesis? G

Yes, and the 4 digits must be at the end of the filename "$"

Not 100% correct, as it will also add parenthesis to "9234", which is obviously not a date, so just keep this in mind.