Search for urls with and without www hostname

www is just one common example of the general case relating to domain vs hostname matching. This is fully supported already and extensively configurable.

Since it’s not working for you, either you have previously configured it to behave in this way, or your system has a problem with the PSL data. I’ve just added a new troubleshooting section to Controlling minimum URL match accuracy for an entry which in turn links to the main documentation page describing what the PSL data is.