feat(db): resolve profile_id via profile_aliases in funnel & conversion

[ayushjhanwar-png]

What

Resolve anonymous profile_id → canonical (backend_userid) at read time via the profile_aliases identity map, so funnels/conversions that start on an anon event (logInInitiate, $ae_first_open, _first_event) and end on an identified event (logIn, trialStarted) stitch into a single user instead of reading as two separate people.

This is the read side of the identity-merge work (write path shipped earlier: forked #322 + proxy alias emit). Nothing read profile_aliases until now.

How

• conversion.service.ts — resolve profile_id at the event-source CTE (buildSingleEventCte) via a shared al alias map (argMax(profile_id, created_at) per alias). start_events/end_events dedup, the ASOF join and the end⊆start prefilter then all use the canonical id automatically.
• funnel.service.ts — resolve at the group level (post-union), so custom events are handled with no special-casing; the time-to-convert path is resolved too.

Gating (no hack — self-gates on data)

There is no env var / allowlist. The resolution is a no-op for projects with no aliases (coalesce(nullIf(al.canonical,''), profile_id) just returns the raw id), so projects without profile_aliases rows are byte-identical to before. The only conditions are correctness, not config:

• profile-level only (session grouping already stitches within a session);
• skipped when cohorts are involved (cohort joins match raw profile_id);
• in conversion, skipped when either event is a custom event (resolving per-CTE would mix raw/resolved); funnel doesn't need this since it resolves after the union.

The raw column is qualified as events.profile_id so the SELECT output alias (also profile_id) doesn't bind into the join key.

Validation (dashreels, dev)

funnel	before	after
logInInitiate → logIn (7d)	0.19%	76.8%
_first_event → logIn (1d)	~0%	71%, median TTC 20s
$ae_first_open → trialStarted (1mo)	~0%	13.3%

Typecheck clean on both files.

Out of scope / follow-ups

• Custom-event and cohort funnels stay unresolved (documented guards) — follow-up if needed.
• Historical cohorts (pre-live-alias) under-resolve due to alias-backfill coverage — separate backfill fix, not a code change.

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