[client] Unexport GetServerPublicKey, add HealthCheck method (#5735)

* Unexport GetServerPublicKey, add HealthCheck method

Internalize server key fetching into Login, Register,
GetDeviceAuthorizationFlow, and GetPKCEAuthorizationFlow methods,
removing the need for callers to fetch and pass the key separately.

Replace the exported GetServerPublicKey with a HealthCheck() error
method for connection validation, keeping IsHealthy() bool for
non-blocking background monitoring.

Fix test encryption to use correct key pairs (client public key as
remotePubKey instead of server private key).

* Refactor `doMgmLogin` to return only error, removing unused response

client/internal/profilemanager/config.go

@@ -777,8 +777,7 @@ func UpdateOldManagementURL(ctx context.Context, config *Config, configPath stri
 	}()
 
 	// gRPC check
-	_, err = client.GetServerPublicKey()
-	if err != nil {
+	if err = client.HealthCheck(); err != nil {
 		log.Infof("couldn't switch to the new Management %s", newURL.String())
 		return nil, err
 	}