feat(spartan): enable inbox bot on next-net and staging

[spalladino]

Stacked on #230.

Enable the Inbox bot on next-net, staging-internal, and staging-public with a conservative steady-state probe configuration.

Context

The fourth Inbox bot flavour is already wired into the current Fast Inbox stack, but every existing network leaves its replica count at zero. A-2020 requires enabling the probe on next-net and both staging networks without carrying the dedicated fast-inbox network load profile into shared environments.

Approach

• Run one durable Inbox bot replica per network.
• Send two mixed-domain messages every 600 seconds, giving each batch one public and one private path while halving the fast-inbox network L1 batch rate.
• Keep completion at PROPOSED but anchor the PXE to the checkpointed tip, avoiding the experimental proposed-tip policy used by the fast-inbox network.
• Keep saturation disabled, retain the 512-message outstanding cap and one-hour timeout, and leave dedicated DA/L2 gas limits unset so the wallet estimates them.
• Deploy in order: next-net, staging-internal, then staging-public, with funding for mnemonic index 7300 and a 24-hour soak before each promotion.

Fixes A-2020

[greptile-apps]

Confidence Score: 5/5

The PR appears safe to merge. No broken bot or deployment path was found.

What we checked:

• Inbox config reaches the bot: Yes. Terraform passes every new value to the inbox chart. The parsers accept PROPOSED, checkpointed, mixed, and zero. The pod also receives its L1 URL and key.
• Staging bots use separate keys: No. Both use index 7300, but each environment loads a different mnemonic secret. Their RPC services and saved data also live in separate namespaces.

Summary

The inbox bot is now enabled in next-net and both staging environments with the same runtime settings. Each environment runs one replica that follows proposed blocks, syncs from the checkpointed tip, and sends small mixed batches.

Diagram

sequenceDiagram
    participant Deploy as deploy_network.sh
    participant TF as Terraform and Helm
    participant Bot as Inbox bot in each namespace
    participant L1 as Sepolia inbox contract
    participant RPC as Namespace RPC and PXE

    Deploy->>TF: "Load each BOT_INBOX_* block"
    TF->>Bot: Start one inbox replica
    Bot->>Bot: Derive keys from the environment mnemonic
    Bot->>L1: Seed L1-to-L2 messages
    loop Every 600 seconds
        Bot->>L1: Send a batch of 2 messages
        Bot->>RPC: Sync to the checkpointed tip
        Bot->>RPC: Consume messages in mixed mode
        RPC-->>Bot: Track completion at PROPOSED
    end
    Bot->>Bot: Fail work that exceeds 3600 seconds

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