Refactor Rust SDK errors to use structs with a kind() method

[heaths]

The conventional #[non_exhaustive] enum Error { ... } pattern appears
safe but creates problems as a library evolves. This PR changes all
error types to the struct-with-kind() pattern, which also aligns with
the Azure SDK for Rust error design.

Why not a flat error enum:

• #[non_exhaustive] on the enum prevents exhaustive matching, but
  individual variants are still fixed. Adding a field to any variant —
  even just to improve an error message with a line number or file path
  — is a breaking change.
• Adding context data is harder than it looks. With a flat enum, new
  fields touch every affected variant and all match arms across the
  codebase. With a struct, new fields are added in one place and callers
  who don't use them are unaffected.
• A single enum conflates all failure modes, making it impossible to
  document or guarantee which variants a given function can actually
  return. Callers must handle unrelated variants they will never see, or
  accept a wildcard arm that silently swallows future additions.

The struct + kind pattern:

Concern	Flat enum	Struct + kind()
Categorization	Match directly on variant	Call .kind() → &*Kind
Adding context	Breaking: add fields to variant	Non-breaking: add fields to struct
non_exhaustive	On enum; variants are fixed	Not needed on struct with only private fields
Simple display	Must match all variants	format!("{err}") — no match needed

Callers who only want to display or propagate an error with ? do not
need to call .kind() at all. Only callers who need to inspect the
failure category call .kind(), and they get a stable, scoped *Kind
enum to match against.

[Copilot]

Pull request overview

Note

Copilot was unable to run its full agentic suite in this review.

Refactors the Rust SDK error model to a structured Error/ErrorKind design (and similar *Kind + error wrapper types), removing thiserror usage and updating call sites, tests, examples, and docs accordingly.

Changes:

• Introduces rust/src/errors.rs with ErrorKind, ProtocolErrorKind, SessionErrorKind, and a shared internal representation for error messages/sources.
• Updates SDK code/tests/examples to match on *.kind() and construct errors via with_message(...) / From<...> conversions.
• Adjusts test configuration to require test-support for selected integration tests; updates editor/LSP configuration.

Reviewed changes

Copilot reviewed 20 out of 21 changed files in this pull request and generated 7 comments.

Show a summary per file

File	Description
rust/tests/session_test.rs	Updates session tests to assert on err.kind() and to_string() instead of enum variants.
rust/tests/protocol_version_test.rs	Updates protocol version tests to match on ErrorKind::Protocol(...).
rust/tests/e2e/session_fs_sqlite.rs	Migrates FS error construction to new FsError/FsErrorKind API.
rust/src/types.rs	Switches duplicate tool handler errors to Error::with_message(ErrorKind::InvalidConfig, ...).
rust/src/tool.rs	Updates tool tests to match on err.kind() (ErrorKind::Json).
rust/src/subscription.rs	Introduces RecvErrorKind + RecvError wrapper and manual Display/Error impls.
rust/src/session_fs.rs	Reworks FS errors into FsErrorKind + FsError wrapper with wire mapping logic.
rust/src/session.rs	Constructs/propagates session errors via ErrorKind::Session(SessionErrorKind::...).
rust/src/resolve.rs	Returns BinaryNotFound via ErrorKind (with optional hint) and updates docs.
rust/src/lib.rs	Moves crate error types out to errors.rs, re-exports them, and updates many signatures to Result<T>.
rust/src/jsonrpc.rs	Updates JSON-RPC parsing/transport errors to new ErrorKind model.
rust/src/errors.rs	Adds new centralized error system (Error, ErrorKind, ProtocolErrorKind, SessionErrorKind, StopErrors, etc.).
rust/src/embeddedcli.rs	Migrates embedded CLI extraction/install errors off thiserror to internal Repr model.
rust/examples/session_fs.rs	Updates example to construct FsError via FsErrorKind.
rust/examples/manual_tool_resume.rs	Adjusts imports due to subscription error type visibility changes.
rust/Cargo.toml	Removes thiserror; gates selected integration tests behind test-support.
.vscode/settings.json	Configures rust-analyzer to use all features and clippy checks.
.github/skills/rust-coding-skill/SKILL.md	Updates Rust skill guidance to reference ErrorKind vs prior Error enum variants.
.github/lsp.json	Adds rust-analyzer to repo LSP configuration.
.github/copilot-instructions.md	Adds guidance to use configured LSP operations (find refs/rename) instead of pattern matching.