Advertising media are PHP scripts within the console, all of the standard output text from that script turns up within the console window as the script is running. Is it feasible for any browser window to similarly receive status reviews within the browser while a extended PHP script is running, rather than getting all of the output left following the script?

Yes. Just call flush() and doctor_flush() periodically. You need to write some output a minimum of every 120 seconds to help keep the bond towards the browser alive.

A tough example:

    while(!$done) {
        //doWork();
        echo number_format(100 * ($workDone/$workTotal)) . "% ";
        flush();
        ob_flush();
    }

Edit: here's a random evidence of reality that works during my env:

print('hello');
print(str_repeat(".\n", 2048));
flush();
//this might be a safe way to only flush the buffer if necessary?
if(ob_get_length())
    ob_flush();
sleep(60);

Yes, one factor you will need to be worried about for those who have an especially lengthy execution time is timing out. This will happen like a PHP timeout or like a browser timeout (generally a couple of minutes).

This PHP documentation about connection handling has a great deal of excellent details about keeping connections alive.