refactor(rename): use "AI observability" for renamed LLM analytics product

[charlescook-ph]

Problem

PostHog renamed the LLM analytics product to AI observability. PostHog Code still showed the old name in several places in the UI, so the copy is now out of date.

Changes

Renamed all user-facing references from "LLM analytics" to "AI observability" (sentence case, matching the other product labels like "Web analytics" / "Session replay"):

• Canonical product label in POSTHOG_PRODUCTS (packages/agent/src/posthog-products.ts) — drives the session "PostHog resources used" product chip.
• Desktop inbox: signal-source label/icon badge, filter dropdown, signal card source line, and the signal-source toggles section header + "Learn about…" link.
• Mobile inbox: signal card source line and filter sheet label.
• Billing: token-spend banner copy (normalized the pre-existing "AI Observability" to sentence case) and the spend-analysis agent prompt.
• Docs URLs updated from /docs/llm-analytics to /docs/ai-observability (the session resources bar already used the new path).

Internal identifiers are intentionally left unchanged: the llm_analytics product id, type unions, API paths (/api/llm_analytics/...), cloud-nav URLs, the /instrument-llm-analytics slash command, and the auto-generated API types in generated.ts.

How did you test this?

• pnpm --filter agent typecheck — clean
• posthog-products.test.ts — 59/59 passing
• spendAnalysisPrompt.test.ts — 21/21 passing (assertion updated to match new prompt text)
• Inbox renderer tests — 84/84 passing
• Verified pre-existing agent/renderer test failures are unrelated (reproduced on a clean tree via git stash)
• Grep confirms no remaining user-facing "LLM analytics" strings (only two intentionally-skipped code comments)

Automatic notifications

• Publish to changelog?
• Alert Sales and Marketing teams?

[greptile-apps]

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