feat: add Livesync replication migration guide and reorganize Migrate…

[arajkumar]

…/Sync nav

• Add new /migrate/livesync-replication guide for near-zero-downtime database migration using the Livesync (Postgres connector) workflow, split across main page, advanced topics, and troubleshooting.
• Deprecate /migrate/live-migration with a callout pointing to the new Livesync replication guide; keep it available for in-flight projects.
• Consolidate the Migrate and Sync top-nav tabs into a single Sync tab whose sidebar groups Sync methods and Migration methods. The split was redundant since both tabs shared the same landing page.
• Update the /migrate overview card so "Migrate my database" links to the new Livesync replication guide.

Describe your changes

What did you change? Why did you change it?

Affected pages

• /build/examples/analyze-blockchain
• /build/examples/analyze-energy-consumption
• /build/examples/analyze-financial-tick-data
• /build/examples/analyze-transport-data
• /build/examples/ingest-real-time-financial-data
• /deploy/tiger-cloud/tiger-cloud-aws/tiger-cloud-extensions/pgvector
• /deploy/tiger-cloud/tiger-cloud-azure/tiger-cloud-extensions/pgvector
• /get-started/choose-your-path/install-timescaledb
• /get-started/quickstart/connect-your-app
• /integrate/code/connect-your-app
• /integrate/connectors/source/sync-from-postgres
• /integrate/observability-alerting/grafana
• /migrate
• /migrate/live-migration
• /migrate/livesync-for-postgresql
• /migrate/livesync-replication
• /migrate/livesync-replication-advanced
• /migrate/livesync-replication-troubleshooting

Related Issues

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Issue: #number

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Project	Deployment	Actions	Updated (UTC)
tiger-data-docs	Ready	Preview, Comment	Jun 23, 2026 10:59am

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2 out of 3 committers have signed the CLA.

✅ isvictorious
✅ atovpeko
❌ arajkumar
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