Why doesn't Webservice testing work? Browser keeps asking for sign in

Prestashop 1.7.5.1. Enabling webservice according to the official tutorial. Stuck here: https://devdocs.prestashop.com/1.7/webservice/tutorials/testing-access/#browser-prompt

Browser keeps asking to enter the key indefinitely:

As you may see, there are 2 notices on the back office: "Check that URL rewriting is available on this server" and "Check that the five methods GET, POST, PUT, DELETE, and HEAD are supported by this server". Could the problem be with that?

I see there's written: "URL rewriting (mod_rewrite) is not active on your server, or it is not possible to check your server configuration". But "YES" is on. So I don't know if it concerns the subject:

By tutorial, "if no permission has been set for the key, then the browser will keep asking you to enter the key indefinitely".

But the key configuration has sufficient permissions:

Any reason why the Webservice testing doesn't work?