fix(forester): retain and reuse proofs across eligibility windows

[sergeytimoshin]

Summary

• retain V2 proofs that finish after the 30-second cache-warming deadline instead of dropping the receiver
• release cache warming at the deadline so proof scheduling can continue, while a bounded collector keeps results for up to 10 minutes
• build reusable proof chains by root linkage, including out-of-order completions, and validate them against the current on-chain root before submission
• keep cache warmups generation-scoped and cancellation-safe
• flush partial proof batches before eligibility ends, refinalize stale eligibility, and bound speculative prewarming

Depends on #2387.

[coderabbitai]

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[sergeytimoshin]

Follow-up fix: 1ecdb0a.

Ready proof prefixes can now be sent while collection continues; cache entries are acknowledged only after confirmation. Cached-send errors remain typed so ForesterNotEligible triggers schedule recovery. Pending collections suppress duplicate speculative chains, out-of-order handoff retains proofs across gaps, and prover payloads no longer include the changing local sequence number. Cached-work metrics now count queue items rather than proof instructions.

Validation: 70 forester library tests passed; cargo clippy -p forester --lib -- -D warnings passed; forester formatting and release build passed.

Devnet canary, 2026-09-24 17:22:41–17:25:37 UTC: updated devnet-1 confirmed 5 cached-proof transactions / 2,500 queue items with zero cached-send failures and zero warming deferrals. Unchanged devnet-2 confirmed no processing transactions in the same interval and logged 84 warming deferrals. This is a short operational canary, not a controlled sustained-throughput benchmark.

Promoted devnet-2 after the canary; both APIs healthy with zero container restarts on the final image. Devnet-2 subsequently confirmed a 500-item batch. Mainnet and the shared prover were not restarted. An initial host-binary/runtime glibc mismatch was rolled back and corrected before the successful canary; final image: light-forester:ready-proof-cache-1ecdb0a24-noble.