sourcegraph-amp: wire thread resume with thread ID persistence

[mafredri]

Problem

Amp stores threads entirely server-side on Sourcegraph's infrastructure. Resume uses amp threads continue [threadId], which is a subcommand rather than a flag. The module currently creates a new thread on every startup by piping the prompt via echo "$PROMPT" | amp. There is no mechanism to capture or reuse a thread ID across restarts.

--type amp is already present. No --type change needed.

Desired outcome

• On cold start: Amp starts a new thread. The thread ID is captured and persisted.
• On warm start: Amp continues the prior thread via amp threads continue <threadId>. The prompt delivery mechanism changes entirely (from stdin pipe to subcommand).
• After feat(coder/modules/agentapi): add state persistence #736 lands: enable_state_persistence = true.

Investigation needed first

Test these approaches for capturing the thread ID:

1. Check if Amp sets an AMP_THREAD_ID environment variable.
2. Parse --stream-json output for a thread/session identifier.
3. Use amp threads list after the first run. Check if it supports machine-readable output.

Also verify:

• What happens with amp threads continue <invalidId>?
• Does amp threads continue work reliably in headless mode via agentapi?

Thread resume requires network connectivity to Sourcegraph servers. Air-gapped environments cannot use it.

Version bump

minor