Only use authenticated endpoints during EE integration testing (#3253)

## Issue Addressed

Failures in our CI integration tests for Geth.

## Proposed Changes

Only connect to the authenticated execution endpoints during execution tests.
This is necessary now that it is impossible to connect to the `engine` api on an unauthenticated endpoint.
See https://github.com/ethereum/go-ethereum/pull/24997

## Additional Info

As these tests break semi-regularly, I have kept logs enabled to ease future debugging.
I've also updated the Nethermind tests, although these weren't broken. This should future-proof us if Nethermind decides to follow suit with Geth

testing/execution_engine_integration/src/execution_engine.rs

@@ -22,7 +22,6 @@ pub struct ExecutionEngine<E> {
     engine: E,
     #[allow(dead_code)]
     datadir: TempDir,
-    http_port: u16,
     http_auth_port: u16,
     child: Child,
 }
@@ -46,16 +45,11 @@ impl<E: GenericExecutionEngine> ExecutionEngine<E> {
         Self {
             engine,
             datadir,
-            http_port,
             http_auth_port,
             child,
         }
     }
 
-    pub fn http_url(&self) -> SensitiveUrl {
-        SensitiveUrl::parse(&format!("http://127.0.0.1:{}", self.http_port)).unwrap()
-    }
-
     pub fn http_auth_url(&self) -> SensitiveUrl {
         SensitiveUrl::parse(&format!("http://127.0.0.1:{}", self.http_auth_port)).unwrap()
     }