Timing of beacon committee selection in a DV

[KaloyanTanev]

Describe the bug
In a distributed validator setup, the endpoint POST /eth/v1/validator/beacon_committee_selections is used to exchange partial selection proofs. At slot start, Nimbus VC requests selection proofs for the next slot, instead of the current.

To Reproduce
Steps to reproduce the behavior:

1. Platform details (OS, architecture): macOS aarch64
2. Branch/commit used: v25.6.0
3. Commands being executed: N/A
4. Relevant log lines: N/A

Additional context
Upon asking for DV selection proof, Nimbus asks for the next slot. We have observed this issue in a mixed DV cluster of 2 Nimbus VCs and 2 Lodestar VCs. Asking for a slot ahead gets the request stuck, as the Lodestar VCs will submit their partial selection proofs in the next slot (12s), during that time the request from Nimbus VC keeps on hanging, as it awaits for threshold of signatures to be reached. By the time Lodestar submits them, a timeout for Nimbus occurs.

Logs from Charon running with Lodestar VC:

09:21:12.042 INFO vapi       Get aggregate beacon committee selection for slot... {"slot": 755156, "proofs_len": 18, "vapi_endpoint": "aggregate_beacon_committee_selections"}

Logs from Charon running with Nimbus VC:

09:21:12.367 INFO vapi       Get aggregate beacon committee selection for slot... {"slot": 755157, "proofs_len": 21, "vapi_endpoint": "aggregate_beacon_committee_selections"}

This is Hoodi network and at 09:21:12 slot 755156 starts.