Sync from docs: add Convex as experimental source database (powersync-docs #456)

[bean1352]

Generated by Claude. Review carefully before merging.

Source docs PR: powersync-ja/powersync-docs#456

What changed in docs

powersync-docs #456 adds comprehensive documentation for Convex as a new experimental source database, covering connection setup (deployment URL + deploy key), a required checkpoint table/mutation, polling-based replication via document_deltas, client UUID ID mapping, Convex-specific Sync Streams patterns, and the Convex mutation write path.

Skill updates in this PR

• skills/powersync/AGENTS.md — added Convex to the preflight database list in the Do/Don't compliance table; added Convex as a named path in Onboarding Playbook step 2 (pointing to powersync-service.md § "Convex Quick Start" and noting no custom REST API needed for writes)
• skills/powersync/references/powersync-service.md — added convex to metadata tags; added Convex Quick Start section covering the powersync_checkpoints table + mutation prerequisite, deploy key permission requirements, self-hosted service YAML (type: convex), client UUID ID mapping, polling latency, and the table-drop limitation
• skills/powersync/references/sync-config.md — added convex to metadata tags; added Convex-Specific Patterns section covering UUID ID mapping, Int64 casting to SQLite integer, Convex Auth JWT subject extraction (substring(auth.user_id(), 1, 32)), and table name qualification, with a full example
• skills/powersync/references/custom-backend.md — added a Convex exception note in the Architecture Recap section clarifying that for Convex the write path uses Convex mutations directly (no REST API), and that Convex Auth requires client_auth.audience: [convex]

Notes for reviewer

• Convex is marked Experimental in the docs; the skill edits reflect this but do not block usage — the agent will surface the experimental status via the Quick Start section warning.
• The onboarding-custom.md reference path was deliberately not modified — Convex does not fit the "custom REST backend" pattern and is now routed through the new Convex-specific bullet in AGENTS.md step 2.
• No new skill file was created for Convex; the existing source-database and sync-config coverage is sufficient for the patterns documented. If a dedicated Convex onboarding reference (parallel to onboarding-supabase.md) is warranted in future, that would be a separate PR.
• The type mapping table from sync/types.mdx (Id→text, Int64→text/INTEGER, Float64→real, Boolean→integer/0/1, Bytes→base64 text, Array/Object/Record→JSON text) is not reproduced in full in the skills — the Sync Streams example covers the actionable casting patterns an agent needs. If reviewers want the full table, it could be added to a dedicated Convex reference file.
• Cloud Dashboard connection flow for Convex was not added to skill files (it mirrors the PowerSync Cloud setup path already described); the docs link in the Quick Start section covers it.

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