event/callback on block update?

You might try a useEffect hook subscribed to the attributes.identifier to call the script.

something like:

function Edit( { attributes, setAttributes } ) {

    useEffect( () => {

      // this will fire whenever the attribute changes.
      thirdPartyScriptFunctionName();

    },[attributes.identifier])

     const onChangeIdentifier = (value) => {
        setAttributes({ identifier: value });
     };

    return (
         <div id = {`embed-${ instanceId }`}>
             {attributes.identifier
         ? 
       <div  
           data-identifier= { attributes.identifier }
        >

        </div>

     : 

        <Placeholder
            instructions={ __( 'Enter identifier.' ) }
        >
            <PlainText
                placeholder={ __(
                        'Enter identifier here…'
                    ) }
                value={ attributes.identifier || '' }
                onChange={ onChangeIdentifier }
            />
       </Placeholder>

    }
     </div>);
}

 export default withInstanceId( Edit );

You’ll need to get the useEffect hook from the wp.element global.

Hope this helps!