Modernize .NET SDK for 3.0.0 with playlist support

[wenbinf]

Prepare PodcastAPI 3.0.0 with all five playlist write operations and .NET 8+ support. Generate the 30 endpoint wrappers, contract fixtures, and README reference from the Listen Notes API specification while preserving existing method names and dictionary parameters.

Changes

• Add CreatePlaylist, UpdatePlaylist, AddPlaylistItem, DeletePlaylistItem, and UpdatePlaylistItemNotes, including PUT support, nested path identifiers, and empty notes/descriptions.
• Replace RestSharp with reusable HttpClient transport, per-client credentials, cancellation, timeouts, and redirects disabled by default. Requests no longer modify caller dictionaries.
• Preserve JSON and quota helpers, match headers case-insensitively, expose buffered response details on HTTP errors, and correct the user agent to podcast-api-dotnet.
• Update dependencies and lockfiles, test .NET 8 and 10 in CI, and separate offline tests from credential-free public mock integration checks.
• Compile generated README examples and verify the packed NuGet artifact through a fresh consumer.

Migration

Requires .NET 8+. The RestSharp-specific client.restClient and response.response fields are replaced by constructor transport options and response.StatusCode / response.Headers. Every non-2xx response now throws. See the README migration notes.

Validation

• 47 offline tests passed on .NET 8 and .NET 10.
• All 30 methods passed against the public mock API, including all five playlist writes.
• Standalone source build and packaged consumer checks passed; generated README examples compile.
• Monorepo generation checks, Django documentation tests, frontend typechecking, and snippet tests passed.
• GitHub CI passed: .NET 8, .NET 10, and public mock integration.
• Production GET smoke: 19 of 21 endpoints returned HTTP 200 with response-shape and quota-header checks passing. SpellCheck and FetchRelatedSearches returned HTTP 401 with the expected PRO/ENTERPRISE plan restriction for the test credential. All requests were guarded as GET-only; no production writes were tested.

NuGet publication is separate. Website SDK availability remains gated at the published 1.1.6 version until 3.0.0 is released.