Builder and proposer preferences are lost on beacon node restart

The validator client submits proposer preferences and builder preferences once per proposal slot within the `SUBMIT_BEFORE_PROPOSAL_SLOTS` window and tracks submissions per dependent root, so a successful submission is never repeated unless the proposer shuffling shifts.

The beacon node keeps preferences in memory only. A restart between the submission and the proposal empties the pool, and peers do not re-gossip preferences they already sent, so bid validation at the proposal fails with `No proposer preferences found` for gossip and builder api bids alike, forcing a self-build even though builders hold the preferences and are bidding.

Options, not mutually exclusive:

- resubmit every slot within the submission window and rely on pool dedup instead of tracking submitted slots in the validator client
- resubmit when the validator client detects a beacon node restart
- persist the preferences pools on the beacon node

Related to #9919 since a combined service would only need the fix once.

Start by tracing the validator client's proposer and builder preference submission tracking and the beacon node's in-memory preference pools. Compare the proposed resubmission, restart detection, and persistence approaches, including the relationship to #9919. Done means preferences remain available after a beacon node restart so gossip and builder API bids validate instead of producing “No proposer preferences found”.

Written by the indexing model from the issue text.