[BE-86] Database index audit on foreign keys and hot query paths

[yusuftomilola]

Overview

Entities across ~20 modules define relations, but there is no evidence of a deliberate indexing pass. Booking conflict checks, availability lookups, and dashboard aggregations all filter on columns that are likely unindexed — these degrade sharply as data grows.

Tasks

• Inventory the slowest/most frequent queries: booking overlap checks, availability by workspace + date range, attendance by user + date, invoice by user + status, notifications by user + read state.
• Add @Index() declarations, including composite indexes matching real filter order (e.g. (workspaceId, startTime, endTime)).
• Ensure every foreign key column has an index — Postgres does not create these automatically.
• Add partial indexes where predicates are selective (e.g. unread notifications).
• Generate a migration and record EXPLAIN ANALYZE before/after in the PR.

Acceptance Criteria

• Migration adds the indexes and runs cleanly.
• The PR shows measured improvement on at least three representative queries against a seeded dataset.
• No sequential scans remain on the booking-overlap query.

Notes for Contributors

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