Why an Apache Directory Password Does Not Protect Forward Proxying
A protected welcome page and an authorized forward-proxy request use different configuration contexts. Put proxy policy in the server or virtual host.
A password prompt on Apache's home page protects that local resource. It does not establish that arbitrary forward-proxy requests require the same login.
.htaccess applies to supported directory configuration; it is not a final filter for every request. ProxyRequests and <Proxy> sections belong in server or virtual-host configuration. Put forward-proxy authorization there, using Apache 2.4 authorization syntax and the required authentication setup.
For a private service, combine the intended client-source and account requirements deliberately. Then examine the virtual host selected by each listener, including default hosts and inherited configuration. Accessing one protected hostname does not establish that another active host has the same proxy restrictions.
ProxyPass serves another role, normally mapping a local namespace to a backend. Adding it does not authorize arbitrary forward destinations.
If you can edit only a site's document files, you may lack the administrative scope to establish this service's access boundary. Obtain the server configuration change or use an approved existing proxy; a directory password cannot substitute for it.