refactor(rig-core)!: migrate examples to integration tests

[gold-silver-copper]

Description

This PR reorganizes a large portion of rig-core's provider coverage by migrating many provider-specific examples into provider-scoped integration tests under rig-core/tests.

The main goal is to keep a smaller set of canonical runnable examples in rig-core/examples while moving provider-specific regression coverage into a structure that is easier to extend, run by provider, and maintain over time.

In addition to the migration itself, this PR:

• adds shared test helpers for streaming, reasoning, structured output, tools, loaders, and provider layout checks
• strengthens several migrated tests so they validate behavior instead of only checking for non-empty responses
• updates the README/docs to reflect that many provider-specific examples now live under tests/
• fixes agent streaming so FinalResponse.response() consistently reflects the concatenated assistant text for the final turn
• updates provider-backed smoke test guidance to use serial ignored runs (-- --ignored --test-threads=1) to reduce quota/rate-limit flakiness
• refreshes some provider model defaults where older aliases/models were no longer reliable for current accounts or local setups

A large part of the diff is mechanical movement/reorganization from examples/ into tests/, rather than entirely new behavior.

Fixes #

Type of change

• Bug fix
• New feature
• Breaking change
• Documentation update

Breaking changes

This PR removes the following public Anthropic constants:

• anthropic::completion::CLAUDE_3_5_SONNET
• anthropic::completion::CLAUDE_3_7_SONNET

Migration path:

• use anthropic::completion::CLAUDE_4_SONNET
• or pass an explicit current Anthropic model string

Testing

Validated locally with:

• cargo test -p rig-core --tests --no-run
• cargo check -p rig-core --examples

Provider-backed smoke tests were also run selectively during development with provider credentials. Whole-provider runs should be executed serially, for example:

• cargo test -p rig-core --test openai -- --ignored --test-threads=1
• cargo test -p rig-core --test anthropic -- --ignored --test-threads=1
• cargo test -p rig-core --test gemini -- --ignored --test-threads=1