[Feature]: [P3] Analytics: per-tool depth splits + exact percentiles (parked remainder; gated on real traffic and the D-1 platform ruling)

Rescoped 2026-07-21 during the full-repository-audit routing pass (report at _bmad-output/planning-artifacts/reviews/full-repository-audit-2026-07-21/): the bulk of the original idea shipped in #531/#533, so this issue now tracks only the parked remainder. Backlog row analytics-tool-depth (parked) mirrors it.

Shipped (no longer this issue's scope)

• #531: per-session placement counting on the build path and the depth events, including tool_session_uses { tool, uses } emitted once per session.
• #533: the aggregate Depth section in the analytics report (p50/p90/max reconstructed from value/count histograms, truncation caveats documented).

Remaining, parked

• Per-tool depth splits: the Vercel aggregate groups by one property at a time, so depth-by-tool cannot be cross-tabulated today.
• Exact percentiles: reconstruction from capped histograms gives lower-bound p90/max; exact per-session quantiles need a session-aware tool (quantile(0.9)(uses) GROUP BY tool is one line in PostHog).

Gates (both must hold before picking this up)

1. Real traffic: ~100-200 sessions per tool so the numbers are signal, not noise (the audit measured roughly a dozen sessions per 30 days).
2. The D-1 analytics-platform ruling (#542): if PostHog is chosen, both remainders become trivial queries and this issue closes into the migration work; if Vercel WA stays, this issue needs its own design for the split (for example a combined tool|uses-band property under the 100-bucket cap).

Original idea (2026-07-21, for the record)

tool_used is a reach metric (fires once per distinct tool per session); the depth signal answers "how heavily do engaged players lean on each tool." Deferred originally because value at current volume was the blocker, performance never was, and the work should be tied to a concrete design question (palette curation, tutorial emphasis).

Start with the audit report at _bmad-output/planning-artifacts/reviews/full-repository-audit-2026-07-21/ and the D-1 platform ruling in #542; review the shipped analytics work in #531 and #533 for context. Do not begin implementation until real traffic reaches the stated threshold and the platform is decided; done means either closing this into migration work or delivering a design for per-tool splits and exact session-aware percentiles.