Bring skills in line with a few recent updates

[benitav]

Brings the skills in line with recent docs updates flagged via drift issues. Each change matches a docs PR that has already merged in https://github.com/powersync-ja/powersync-docs.

• Kotlin SDK — Room integration is now Beta. Resolves [Drift] Kotlin SDK Room integration promoted from alpha to beta (powersync-kotlin #346) #28. Source: Mark Room integration as beta powersync-docs#445.
• Kotlin SDK — drop CocoaPods setup for powersync-sqlite-core. From v1.12.0+ the extension is statically linked into com.powersync:core for all Apple targets. Resolves [Drift] Kotlin SDK v1.12.0 statically links core extension — CocoaPods setup instruction is now wrong (powersync-kotlin #344) #22. Source: Kotlin SDK v1.12.0 updates powersync-docs#435.
• JS SDK — rename "Diagnostics App" to "Sync Diagnostics Client". Resolves [Drift] "Diagnostics App" terminology renamed to "Sync Diagnostics Client" (powersync.dart #413) #24. Source: Rename diagnostics app to sync diagnostics client powersync-docs#259.
• .NET — document built-in attachment queue. Resolves [Drift] Offline-first file attachments helper added to .NET SDK (powersync-dotnet #68) #21. Source: Document new attachment functionality for .NET powersync-docs#437.
• Legacy sync clients removed — JS, Kotlin, and Swift. Updated the JS internals note (the legacy JS client is removed, not deprecated) and dropped the now-defunct newClientImplementation: false debug technique. Resolves [Drift] JavaScript sync client removed — stale "deprecated" language in JS SDK reference (powersync-js #938) #23. Sources: Remove JavaScript sync client powersync-js#938, Polish documentation for new sync client implementation powersync-swift#131.

Issue #20 (Swift native rewrite) was left open — the corresponding docs updates have not shipped yet.

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AI disclosure: this PR was prepared with Claude Code. Each change was cross-referenced against a merged docs PR before applying.