pip search does not work *via* NXRM PyPI proxy to NXRM PyPI repository and authentication is required

SYMPTOM:

"pip download" works but "pip search" (which uses POST) does not work if this pipy proxy repository's remote URL is another Nexus pipy repository (proxy, hosted).

REPRODUCE STEPS:

1. Create a pypi proxy repo "pypi-proxy-proxy" which points to another "pypi-proxy" (disabled TTLs for testing purpose)

           {
               "attributes": {
                   "proxy": {
                       "remoteUrl": "http://localhost:8081/repository/pypi-proxy",
                       "contentMaxAge": 0,
                       "metadataMaxAge": 0
                   },
                   "httpclient": {
                       "blocked": false,
                       "autoBlock": false,
                       "authentication": {
                           "type": "username",
                           "username": "admin",
                           "password": "admin123"
                       }
                   },
                   "storage": {
                       "blobStoreName": "default",
                       "strictContentTypeValidation": true
                   },
                   "negativeCache": {
                       "enabled": false,
                       "timeToLive": 1440
                   },
                   "cleanup": {
                       "policyName": []
                   }
               },
               "name": "pypi-proxy-proxy",
               "format": "",
               "type": "",
               "url": "",
               "online": true,
               "routingRuleId": "",
               "authEnabled": true,
               "httpRequestSettings": false,
               "recipe": "pypi-proxy"
           }
   

2. Disable Anonymous
3. Confirm download works

   pip -v download -i http://admin:admin123@localhost:8081/repository/pypi-proxy-proxy/simple Django
   

4. Try search and fails

   pip -v search -i http://admin:admin123@localhost:8081/repository/pypi-proxy-proxy/pypi Django
   

5. Test against the remote URL (pypi-proxy)

   pip -v search -i http://admin:admin123@localhost:8081/repository/pypi-proxy/pypi Django
   

EXPECTED BEHAVIOUR:

Same as "pip download", "pip search" should work.

ACUTUAL BEHAVIOUR:

Pip returns "pip._internal.exceptions.NetworkConnectionError: 502 Server Error: Bad Gateway"
Nexus log shows:

2020-12-11 05:17:20,334+0000 WARN  [qtp1037423558-947] node-nxrm-ha1.standalone.localdomain admin org.sonatype.nexus.repository.pypi.internal.orient.OrientPyPiProxyFacetImpl - Exception org.apache.http.client.ClientProtocolException checking remote for update, proxy repo pypi-hosted-proxy failed to fetch pypi, content not in cache.
org.apache.http.client.ClientProtocolException: null

It seems current HttpClient used by org.sonatype.nexus.repository.proxy.ProxyFacetSupport#fetch(java.lang.String, org.sonatype.nexus.repository.view.Context, org.sonatype.nexus.repository.view.Content) does not work with POST + Basic Authentication.
Enabling DEBUG logging shows:

Caused by: org.apache.http.client.NonRepeatableRequestException: Cannot retry request with a non-repeatable request entity.
        at org.apache.http.impl.execchain.MainClientExec.execute(MainClientExec.java:225)
        at org.apache.http.impl.execchain.ProtocolExec.execute(ProtocolExec.java:186)
        at org.apache.http.impl.execchain.RetryExec.execute(RetryExec.java:89)
        at org.apache.http.impl.execchain.RedirectExec.execute(RedirectExec.java:110)
        at org.apache.http.impl.client.InternalHttpClient.doExecute(InternalHttpClient.java:185)
        ... 146 common frames omitted