Problem

The Anthropic instrumentation merges the top-level system param into the logged input messages array (since the Anthropic API takes it separately rather than as a message). But coalesceInput appends it after the conversation messages, so every anthropic.messages.create span logs:

[
  { "role": "user", "content": "..." },
  { "role": "system", "content": "..." }
]

This doesn't match what the model actually receives (the API applies the system prompt first), and it makes logged calls awkward to reuse: opening a logged span in the playground requires manually reordering the messages before rerunning, since chat-message convention puts system first.

Fix

coalesceInput now prepends the system message instead of appending it. Logged inputs read [system, user, ...].

• Exported coalesceInput and added unit tests (system-first ordering, system as text-block array, no system prompt, no mutation of the caller's array) — it previously had no direct coverage.
• Regenerated the anthropic-instrumentation e2e span-tree snapshots via test:e2e:update; the diffs are purely the system message moving from last to first.

Verification

• js/ core suite: 1070 passed
• anthropic-instrumentation e2e scenario run twice: 184 passed both times
• tsc --noEmit and prettier clean

Note: this changes the logged input shape, so anything downstream that assumes the system message is last (e.g. saved playground sessions or scorers parsing input) will see the new order. The in-repo e2e assertions already look up the system message by role rather than position, so none needed changes.

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