Lodestar v1.47.0 with ethpillar and CSM Nimbus: Nimbus validator client fails with "Could not obtain time configuration parameters"

### Describe the bug

I am not really sure where the bug lies but I believe it's coming from Lodestar.

### Describe the bug

After upgrading Lodestar consensus client from v1.45.0 to v1.47.0, the Nimbus validator client (used in ethpillar for CSM validator duties) fails to initialise.

Nimbus exits almost immediately with:

Validator client initialization failed err_name=ValidatorClientError err_msg="Could not obtain time configuration parameters"

The validator service then crash-loops.

### Versions tested

| Nimbus validator | Lodestar consensus | Result |
|---|---|---|
| v26.7.0 | 1.45.0 | works |
| v26.8.0 | 1.45.0 | works |
| v26.7.0 | 1.47.0 | fails |
| v26.8.0 | 1.47.0 | fails |

### Workaround

Roll back Lodestar consensus client to v1.45.0 and everything goes back to normal.

### Expected behavior

Nimbus validator client should connect to Lodestar’s Beacon API and initialise normally with Lodestar v1.47.0, as it does with Lodestar v1.45.0.

### Steps to reproduce

- Network: Ethereum mainnet
- Consensus client: Lodestar v1.47.0
- Validator client: Nimbus v26.8.0 and v26.7.0
- Orchestration: ethpillar
- Execution client: Besu
- OS: Debian 13

### Additional context

### Logs
```bash
Sep 08 19:56:01 node nimbus_validator_client[3478491]: NTC 2026-09-08 19:56:01.887+02:00 Beacon node initialized node=http://127.0.0.1:5052 node_index=0 node_roles=AGBSDT
Sep 08 19:56:01 node nimbus_validator_client[3478491]: INF 2026-09-08 19:56:01.887+02:00 Initializing genesis nodes_count=1
Sep 08 19:56:01 node nimbus_validator_client[3478491]: ERR 2026-09-08 19:56:01.899+02:00 Validator client initialization failed err_name=ValidatorClientError err_msg="Could not obtain time configuration parameters"
Sep 08 19:56:01 node systemd[1]: csm_nimbusvalidator.service: Deactivated successfully.
Sep 08 19:56:07 node systemd[1]: csm_nimbusvalidator.service: Scheduled restart job, restart counter is at 441.
Sep 08 19:56:07 node systemd[1]: Started csm_nimbusvalidator.service - Nimbus CSM Validator Client.
Sep 08 19:56:07 node nimbus_validator_client[3478614]: NTC 2026-09-08 19:56:07.123+02:00 Launching validator client version=v26.8.0-404a00-stateofus cmdParams="["--data-dir=/opt/ethpillar/plugin-csm/csm_nimbus_validator", "--payload-builder=true", "--beacon-node=http://127.0.0.1:5052", --metrics, "--metrics-port=8108", "--metrics-address=127.0.0.1", "--suggested-fee-recipient=0xxxxxxx", "--graffiti=\x", "--doppelganger-detection=off", --non-interactive]" config="(configFile: none(InputFile), logLevel: INFO, logFormat: auto, dataDirFlag: some(/opt/ethpillar/plugin-csm/csm_nimbus_validator), doppelgangerDetection: false, nonInteractive: true, validatorsDirFlag: none(InputDir), verifyingWeb3Signers: [], provenBlockProperties: [], web3signerUpdateInterval: 3600, web3Signers: [], secretsDirFlag: none(InputDir), restRequestTimeout: 0, restMaxRequestBodySize: 16384, restMaxRequestHeadersSize: 64, suggestedFeeRecipient: some(0xxxxxxxx), suggestedGasLimit: 60000000, keymanagerEnabled: false, keymanagerPort: 5062, keymanagerAddress: 127.0.0.1, keymanagerAllowedOrigin: none(string), keymanagerTokenFile: none(InputFile), metricsEnabled: true, metricsAddress: 127.0.0.1, metricsPort: 8108, graffiti: some(0xxxxxx), stopAtEpoch: 0, payloadBuilderEnable: true, distributedEnabled: false, builderBoostFactor: 100, beaconNodes: [http://127.0.0.1:5052], beaconNodeMode: bestscore, monitoringType: event, batchAttestations: false, logFile: none(OutFile))" beacon_nodes_count=1
```

### Operating system

Linux

### Lodestar version or commit hash

v1.47.0

Start by reproducing the v1.45.0 versus v1.47.0 comparison using Nimbus against Lodestar’s Beacon API at http://127.0.0.1:5052. Trace the time-configuration request during Nimbus initialization and compare the API behavior or responses between versions. Done means Nimbus v26.7.0 and v26.8.0 initialize normally with Lodestar v1.47.0 without crash-looping.

Written by the indexing model from the issue text.